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Call number: | 9783319461434:ONLINE Show nearby items on shelf |
Title: | The Universal Coefficient Theorem and Quantum Field Theory A Topological Guide for the Duality Seeker |
Author(s): |
Andrei-Tudor Patrascu |
Date: | 2017 |
Size: | 1 online resource (XVI, 270 p. 6 illus., 1 illus. in color p.) |
Contents: | Introduction -- Elements of General Topology -- Algebraic Topology -- Homological Algebra -- Connections: Topology and Analysis -- The Atyiah Singer Index Theorem -- Universal Coeﬃcient Theorems -- BV and BRST Quantization, Quantum |
Observables and Symmetry -- Universal Coeﬃcient Theorem and Quantum Field Theory -- The Universal Coeﬃcient Theorem and Black Holes -- From Grothendieck’s Schemes to QCD -- Conclusions. | |
ISBN: | 9783319461434 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Physics , Mathematical physics , Algebraic topology , Quantum field theory , String theory , Elementary particles (Physics) , Physics , Quantum Field Theories, String Theory , Algebraic Topology , Mathematical Applications in the Physical Sciences , Elementary Particles, Quantum Field Theory |
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Call number: | 9783319419176:ONLINE Show nearby items on shelf |
Title: | An Introduction to the Language of Category Theory |
Author(s): |
Steven Roman |
Date: | 2017 |
Size: | 1 online resource (XII, 169 p. 176 illus., 5 illus. in color p.) |
Contents: | Preface -- Categories -- Functors and Natural Transformations -- Universality -- Cones and Limits -- Adjoints -- References -- Index of Symbols -- Index |
ISBN: | 9783319419176 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Algebra , Ordered algebraic structures , Mathematics , Category Theory, Homological Algebra , Order, Lattices, Ordered Algebraic Structures , General Algebraic Systems |
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Call number: | SPRINGER-2016-9784431560562:ONLINE Show nearby items on shelf |
Title: | Structural Analysis of Metallic Glasses with Computational Homology |
Author(s): |
Akihiko Hirata |
Date: | 2016 |
Size: | 1 online resource (7 p.) |
Note: | 10.1007/978-4-431-56056-2 |
Contents: | 1. Introduction -- 2. Metallic glasses -- 2.1. What is glass? -- 2-2. Structure and properties of metallic glasses -- 2-3. Structure determination and its difficulty -- 3. Homology and computational homology -- 3.1. Cubical complex -- 3.2. Cubical homology -- 3.3. Computing homology groups -- 4. Structure analysis of metallic glasses -- 4.1. Advantage of computational homology -- 4.2. Preparation of input data for metallic glasses -- 4.3. Computing procedure for metallic glasses -- 4.4. Interpretat ion of results obtained by computational homology -- 5. Appendix |
ISBN: | 9784431560562 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | SpringerBriefs in the Mathematics of Materials: 2 |
Keywords: | Mathematics , Chemometrics , Category theory (Mathematics) , Homological algebra , Mathematical physics , Mathematics , Mathematical Applications in the Physical Sciences , Category Theory, Homological Algebra , Math. Applications in Chemistry |
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Call number: | SPRINGER-2016-9783662493618:ONLINE Show nearby items on shelf |
Title: | Topologie algébrique Chapitres 1 à 4 |
Author(s): |
N Bourbaki |
Date: | 2016 |
Size: | 1 online resource (498 p.) |
Note: | 10.1007/978-3-662-49361-8 |
Contents: | Mode d'Emploi -- Introduction -- Chapitre I. Revêtements -- 1. Produits fibrés et carrés cartésiens -- 2. Applications étales -- 3. Faisceaux -- 4. Revêtements -- 5. Revêtements principaux -- 6. Espaces simplement connexes -- Exercices -- Ch apitre II. Groupoïdes -- 1. Carquois -- 2. Graphes -- 3. Groupoïdes -- 4. Homotopies -- 5. Coégalisateur -- Exercices -- Chapitre III. Homotopie et Groupoïdes de Poincaré -- 1. Homotopies, homéotopies -- 2. Homotopie et chemins -- 3. Groupoïde de P oincaré -- 4. Homotopie et revêtements -- 5. Homotopie et revêtements (cas des espaces localement connexes par arcs) -- Exercices -- Chapitre IV. Espaces Delaçables -- 1. Espaces délaçables -- 2. Groupes de Poincaré des espaces délaçables -- 3. G roupes de Poincaré des groupes topologiques -- 4. Théorie de la descente -- 5. Théorème de van Kampen -- 6. Espaces classifiants -- Exercices -- Index des notations -- Index terminologique |
ISBN: | 9783662493618 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Group theory , Algebraic topology , Manifolds (Mathematics) , Complex manifolds , Mathematics , Algebraic Topology , Category Theory, Homological Algebra , Manifolds and Cell Complexes (incl. Diff.Topology) , Group Theory and Generalizations |
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Call number: | SPRINGER-2016-9783658106331:ONLINE Show nearby items on shelf |
Title: | Manifolds, Sheaves, and Cohomology |
Author(s): |
Torsten Wedhorn |
Date: | 2016 |
Size: | 1 online resource (354 p.) |
Note: | 10.1007/978-3-658-10633-1 |
Contents: | Topological Preliminaries -- Algebraic Topological Preliminaries -- Sheaves -- Manifolds -- Local Theory of Manifolds -- Lie Groups -- Torsors and Non-abelian Cech Cohomology -- Bundles -- Soft Sheaves -- Cohomology of Complexes of Sheaves -- Cohom ology of Sheaves of Locally Constant Functions -- Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis |
ISBN: | 9783658106331 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Topological groups , Lie groups , Global analysis (Mathematics) , Manifolds (Mathematics) , Differential geometry , Mathematics , Category Theory, Homological Algebra , Topological Groups, Lie Groups , Differential Geometry , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9783319264370:ONLINE Show nearby items on shelf |
Title: | Minimal Free Resolutions over Complete Intersections |
Author(s): |
David Eisenbud |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (107 p.) |
Note: | 10.1007/978-3-319-26437-0 |
ISBN: | 9783319264370 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2152 |
Keywords: | Mathematics , Algebraic geometry , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Physics , Mathematics , Commutative Rings and Algebras , Algebraic Geometry , Category Theory, Homological Algebra , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-2016-9783319259017:ONLINE Show nearby items on shelf |
Title: | Perturbative Algebraic Quantum Field Theory An Introduction for Mathematicians |
Author(s): |
Kasia Rejzner |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (180 p.) |
Note: | 10.1007/978-3-319-25901-7 |
Contents: | Introduction -- Algebraic approach to quantum theory -- Algebraic quantum mechanics -- Causality -- Haag-Kastler axioms -- pAQFT axioms -- LCQFT -- Kinematical structure -- The space of field configurations -- Functionals on the |
configuration space -- Fermionic field configurations -- Vector fields -- Functorial interpretation -- Classical theory -- Dynamics -- Natural Lagrangians -- Homological characterization of the solution space -- The net of topological | |
Poisson algabras -- Analogy with classical mechanics -- Deformation quantization -- Star products -- The star product on the space of multivector fields -- Kähler structure -- Interaction -- Outline of the approach -- Scatering matrix | |
and time ordered products -- Renormalization group -- Interacting local nets -- Explicit construction -- Gauge theories -- Classical gauge theory -- Gauge-fixing -- BV formalism -- Effective quantum gravity -- From LCQFT to quantum | |
gravity -- Dynamics and symmetries -- Linearized theory -- Quantization -- Relational observables -- Background independence | |
ISBN: | 9783319259017 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Algebra , Field theory (Physics) , Mathematical physics , Quantum field theory , String theory , Physics , Quantum Field Theories, String Theory , Mathematical Physics , Field Theory and Polynomials |
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Call number: | SPRINGER-2016-9783319234885:ONLINE Show nearby items on shelf |
Title: | Homotopical Topology |
Author(s): |
Anatoly Fomenko |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (627 p.) |
Note: | 10.1007/978-3-319-23488-5 |
Contents: | Introduction -- Homotopy -- Homology -- Spectral Sequences of Fibrations -- Cohomology Operations -- The Adams Spectral Sequence -- K-Theory and Other Extraordinary Cohomology Theories |
ISBN: | 9783319234885 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 273 |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , K-theory , Algebraic topology , Mathematics , Category Theory, Homological Algebra , K-Theory , Algebraic Topology |
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Call number: | SPRINGER-2014-9788132215998:ONLINE Show nearby items on shelf |
Title: | Basic Modern Algebra with Applications [electronic resource] |
Author(s): |
Mahima Ranjan Adhikari Avishek Adhikari |
Date: | 2014 |
Publisher: | New Delhi : Springer India : Imprint: Springer |
Size: | 1 online resource |
Note: | The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a waythat it encourages ind ependent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. Inaddition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theoryto structure theory of rings and homological algebra. Algebraic as pects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraictopology, category theory, algebraic geometry, algebraic number theory, cryptography and theo retical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, withthe help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, example s, exercises and historical notes represents a valuable and unique resource |
Contents: | Prerequisites: Basics of Set Theory and Integers |
Groups: Introductory Concepts | |
Actions of Groups, Topological Groups and semigroups | |
Rings: Introductory Concepts | |
Ideals of Rings: Introductory concepts | |
Factorization in Integral Domains and in Polynomial Rings | |
Rings with Chain Conditions | |
Vector Spaces | |
Modules | |
Algebraic Aspects of Number Theory | |
Algebraic Numbers | |
Introduction to Mathematical Cryptography | |
Appendix A: Some Aspects of Semirings | |
Appendix B: Category Theory | |
Appendix C: A Brief Historical Note | |
ISBN: | 9788132215998 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Number theory |
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Call number: | SPRINGER-2014-9783319079684:ONLINE Show nearby items on shelf |
Title: | Representation Theory [electronic resource] : A Homological Algebra Point of View |
Author(s): |
Alexander Zimmermann |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra andrepresentations of groups to block the ory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more generalalgebras, such as symmetric finite dimensional algebras over a fie ld. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their maininvariants and links between them. Group theoretical applications of these theories are given such as the structure of blocks of cyclic defect groups whenever appropriate. Overall, many methods from the representation theory ofalgebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields, and guides the reader in the use of categorical equivalences in the representation theory of groups andalgebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use |
Contents: | Rings, Algebras and Modules |
Modular Representations of Finite Groups | |
Abelian and Triangulated Categories | |
Morita theory | |
Stable Module Categories | |
Derived Equivalences | |
ISBN: | 9783319079684 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Algebra and Applications, 1572-5553 : v19 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2014-9783319029528:ONLINE Show nearby items on shelf |
Title: | Advances in Lie Superalgebras [electronic resource] |
Author(s): |
Maria Gorelik Paolo Papi |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The volume is the outcome of the conference Lie superalgebras, which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held providedcomprehensive insights into the n ewest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field andprovides a complete account of the newest trends in r esearch on Lie Superalgebras |
Contents: | 1 A. Alldridge, Z. Shaikh: Superbosonisation, Riesz superdistributions, and highest weight modules |
2 K. Coulembier: Homological algebra for osp(1|2n) | |
3 A. DAndrea: Finiteness and orbifold vertex operator algebras | |
4 A. De Sole: On classical finite and affine W | |
algebras | |
5 M. Gorelik, D. Grantcharov: Q | |
type Lie superalgebras | |
6 C. Hoyt: Weight modules for the Lie superalgebra D(2,1,a) | |
7 R. Fioresi, S. Kwok: On SUSY curves | |
8 V. G. Kac, P. Moseneder Frajria, P. Papi: Dirac operators and the Very Strange Formula for Lie superalgebras | |
9 V. Mazorchuk: Parabolic category O fo | |
ISBN: | 9783319029528 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer INdAM Series, 2281-518X : v7 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topology |
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Call number: | SPRINGER-2014-9781493909254:ONLINE Show nearby items on shelf |
Title: | Commutative Algebra [electronic resource] : Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions |
Author(s): |
Marco Fontana Sophie Frisch Sarah Glaz |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point tofuture directions of rese arch in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics andresearch methods include Noetherian and non- Noetheri an ring theory as well as integer-valued polynomials and functions. Specific topics include: Homological dimensions of Prfer-like rings Quasi complete rings Total graphs of rings Properties of prime ideals over various rings Bases for integer-valued p olynomials Boolean subrings The portable property of domains Probabilistic topics inIntn(D) Closure operations in Zariski-Riemann spaces of valuation domains Stability of domains Non-Noetherian grade Homotopy in integer-valued polynomials Localiza tions of global propertiesof rings Topics in integral closure Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees ofthe conferen ce in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Grazconference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere |
Contents: | Preface |
Weak global dimension of Prfer | |
like rings (K. Adarbeh, S | |
E. Kabbaj) | |
Quasi | |
complete semilocal rings and modules (D.D. Anderson) | |
On the total graph of a ring and its related graphs: A survey (A. Badawi) | |
Prime ideals in polynomials and power series rings over Noetherian domains | |
Integer | |
valued polynomials: Looking for regular bases (J | |
L. Chabert) | |
On Boolean subrings of rings (I. Chajda, G. Eigenthaler) | |
On a new class of integral domains with the portable property (D.E. Dobbs, G. Picavet, M. Picavet | |
L'Hermitte) | |
The probability that Intn(D) is free (J. Elliott | |
ISBN: | 9781493909254 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Algebraic topology |
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Call number: | SPRINGER-2013-9781461452928:ONLINE Show nearby items on shelf |
Title: | Commutative Algebra [electronic resource] : Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday |
Author(s): |
Irena Peeva |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, includingcore areas in Commutati ve Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit ofjunior mathematicians and researchers who are n ew to the field it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many openproblems are discussed with the aspiration to inspire the readers and foster further research |
Note: | Springer eBooks |
Contents: | Marian Aprodu: Lazarfeld |
Mukai bundles and applications to syzygies | |
Paul Aspinwall: Some Applications of Commutative Algebra to String Theory | |
Angelica Benito, Eleonore Faber, and Karen Smith: Measuring singularities with Frobenius: the basics | |
Christine Berkesch, Daniel Erman, and Manoj Kumini: Three avors of extremal Betti tables | |
Manuel Blickle and Karl Schwede: p1 linear maps in algebra and geometry | |
Markus Brodmann, Cao Luy Linh, and Maria | |
Helena Seiler: Castelnuovo | |
Mumford Regularity of Annihilators, Ext | |
Modules and Tor | |
Modules | |
David Buchsbaum: Selections From the Letter | |
Pl | |
ISBN: | 9781461452928 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra |
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Call number: | SPRINGER-2013-9781447148296:ONLINE Show nearby items on shelf |
Title: | Algebraic Geometry and Commutative Algebra [electronic resource] |
Author(s): |
Siegfried Bosch |
Date: | 2013 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover,Grothendiecks schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved theway to spectacular progress such as the proof of Fermats Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broadentheir view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter ofthe book is preceded by a motivating introduction with an informal discussion of the contents. Typical exa mples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourselfor for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature |
Note: | Springer eBooks |
Contents: | Rings and Modules |
The Theory of Noetherian Rings | |
Integral Extensions | |
Extension of Coefficients and Descent | |
Homological Methods: Ext and Tor | |
Affine Schemes and Basic Constructions | |
Techniques of Global Schemes | |
Etale and Smooth Morphisms | |
Projective Schemes and Proper Morphisms | |
ISBN: | 9781447148296 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra |
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Call number: | SPRINGER-2012-9783834883308:ONLINE Show nearby items on shelf |
Title: | Lectures on Algebraic Geometry I [electronic resource] : Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces |
Author(s): |
Gnter Harder |
Date: | 2012 |
Edition: | 2nd revised Edition |
Publisher: | Wiesbaden : Vieweg+Teubner Verlag |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods areindispensable for modern alge braic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compactRiemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them |
Note: | Springer eBooks |
ISBN: | 9783834883308 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry |
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Call number: | SPRINGER-2012-9783642303623:ONLINE Show nearby items on shelf |
Title: | Algebraic Operads [electronic resource] |
Author(s): |
Jean-Louis Loday Bruno Vallette |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In many areas of mathematics some higher operations are arising. These have become so important that several research projects refer to such expressions. Higher operations form new types of algebras. The key tounderstanding and comparing them, to cre ating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such asalgebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study allkinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a concept ual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality forassociative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected to be familiarwith elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and num erous figures are included. After an elementary chapter on classical algebra, accessible toundergraduate students,the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three ap pendices review the basic results needed in order to understand thevarious chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, thebook can also be used as a reference work by researchers. |
Note: | Springer eBooks |
Contents: | Preface |
1.Algebras, coalgebras, homology | |
2.Twisting morphisms | |
3.Koszul duality for associative algebras | |
4.Methods to prove Koszulity of an algebra | |
5.Algebraic operad | |
6 Operadic homological algebra | |
7.Koszul duality of operads | |
8.Methods to prove Koszulity of an operad | |
9.The operads As and A\infty | |
10.Homotopy operadic algebras | |
11.Bar and cobar construction of an algebra over an operad | |
12.(Co)homology of algebras over an operad | |
13.Examples of algebraic operads | |
Apendices: A.The symmetric group | |
B.Categories | |
C.Trees | |
References | |
Index | |
List of Not | |
ISBN: | 9783642303623 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v346 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Algebraic topology , Cell aggregation Mathematics |
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Call number: | SPRINGER-2012-9783642227165:ONLINE Show nearby items on shelf |
Title: | The Schringer-Virasoro Algebra [electronic resource] |
Author(s): |
Jie Unterberger Claude Roger |
Date: | 2012 |
Publisher: | Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Monograph |
Note: | Springer 2012 Physics and Astronomy eBook collection |
Note: | Springer e-book platform |
ISBN: | 9783642227165 |
Series: | Texts and Monographs in Physics |
Series: | e-books |
Keywords: | Mathematical Methods in Physics , Topological Groups, Lie Groups , Mathematical Physics , Category Theory, Homological Algebra , Statistical Physics, Dynamical Systems and Complexity |
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Call number: | SPRINGER-2012-9783642192258:ONLINE Show nearby items on shelf |
Title: | A Royal Road to Algebraic Geometry [electronic resource] |
Author(s): |
Audun Holme |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to readall of his work Eleme nts. Euclid is said to have answered: There is no royal road to geometry! The book starts by explaining this enigmatic answer, the aim of the book being to argue that indeed, in some sense there is a royalroad to algebraic geometry. From a point of depart ure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendiecks theory of schemes. Contemporary homological tools areexplained. The reader will follow a directed path leading up to the main elem ents of modern algebraic geometry. When the road is completed, the reader is empowered to start navigating in this immense field, and to open up the door to awonderful field of research. The greatest scientific experience of a lifetime! |
Note: | Springer eBooks |
Contents: | Part I Curves: 1 Affine and Projective Space |
2 Curves in A2 k and in P2 | |
3 Higher Geometry in the Projective Plane | |
4 Plane Curves and Algebra | |
5 Projective Varieties in PNk | |
Part II Introduction to Grothendiecks Theory of Schemes: 6 Categories and Functors | |
7 Constructions and Representable Functors | |
8 Abelian Categories | |
9 The Concept of Spec(A) | |
10 The Category of Schemes | |
11 Properties of Morphisms of Schemes | |
12 Modules, Algebras and Bundles on a Scheme | |
13 More Properties of Morphisms, Scheme Theoretic Image and the Sorite | |
14 Projective Schemes and Bu | |
ISBN: | 9783642192258 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , Geometry , Algebraic topology |
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Call number: | SPRINGER-2012-9781447143932:ONLINE Show nearby items on shelf |
Title: | The Local Structure of Algebraic K-Theory [electronic resource] |
Author(s): |
Bjrn Ian Dundas Thomas G Goodwillie Randy McCarthy |
Date: | 2012 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerfulmathematical object is ve ry hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homologicalinvariants offered by motivic cohomology and topo logical cyclic homology. This book covers the connection between algebraic K-theory and Bkstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference betweenthe theories are locally constant. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain ahost of nearby calculations in K-theory. For instance, Quillen's calculation of the K-theory of fini te fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers giveinsight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local corresponden ce between K-theory and topological cyclic homology, the book provides an introduction to the necessarybackground in algebraic K-theory and highly structured homotopy theory collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in thefield. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology |
Note: | Springer eBooks |
Contents: | Algebraic K |
theory | |
Gamma | |
spaces and S | |
algebras | |
Reductions | |
Topological Hochschild Homology | |
The Trace K THH | |
Topological Cyclic Homology | |
The Comparison of K | |
theory and TC | |
ISBN: | 9781447143932 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algebra and Applications, 1572-5553 : v18 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , K-theory , Algebraic topology |
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Call number: | SPRINGER-2012-9781447122944:ONLINE Show nearby items on shelf |
Title: | Syzygies and Homotopy Theory [electronic resource] |
Author(s): |
F.E.A Johnson |
Date: | 2012 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivialfundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematicrehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. Theinnovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation these are confronted in the second, practical, part of the book. Inparticular, the second part of the book considers how the theory works out in detail for the specific e xamples Fn F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms ofthe more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potentialapplications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of inte rest to researchers and also to graduate students with a background in algebra andalgebraic topology |
Note: | Springer eBooks |
Contents: | Preliminaries |
The restricted linear group | |
The calculus of corners and squares | |
Extensions of modules | |
The derived module category | |
Finiteness conditions | |
The Swan mapping | |
Classification of algebraic complexes | |
Rings with stably free cancellation | |
Group rings of cyclic groups | |
Group rings of dihedral groups | |
Group rings of quaternionic groups | |
Parametrizing W1 (Z) : generic case | |
Parametrizing W1 (Z) : singular case | |
Generalized Swan modules | |
Parametrizing W1 (Z) : G = C F | |
Conclusion | |
ISBN: | 9781447122944 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algebra and Applications, 1572-5553 : v17 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2011-9783642110368:ONLINE Show nearby items on shelf |
Title: | Some Aspects of Ring Theory [electronic resource] |
Author(s): |
I. N Herstein |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | S. Amitsur: Associative rings with identities.- I.N. Herstein: Topics in ring theory.- N. Jacobson: Representation theory of Jordan algebras.- I. Kaplansky: The theory of homological dimension.- D. Buchsbaum: Complexes in localring theory.- P.H. Cohn : Two topics in ring theory.- A.W. Goldie: Non-commutative localisation |
Note: | Springer eBooks |
Contents: | S. Amitsur: Associative rings with identities |
I.N. Herstein: Topics in ring theory | |
N. Jacobson: Representation theory of Jordan algebras | |
I. Kaplansky: The theory of homological dimension | |
D. Buchsbaum: Complexes in local ring theory | |
P.H. Cohn: Two topics in ring theory | |
A.W. Goldie: Non | |
commutative localisation | |
ISBN: | 9783642110368 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v37 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Differential equations, partial |
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Call number: | SPRINGER-2011-9783642109799:ONLINE Show nearby items on shelf |
Title: | Categories and Commutative Algebra [electronic resource] |
Author(s): |
P Salmon |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | L. Badescu: Sur certaines singularits des varits algbriques.- D.A. Buchsbaum: Homological and commutative algebra.- S. Greco: Anelli Henseliani.- C. Lair: Morphismes et structures algbriques.- B.A. Mitchell:Introduction to category theory and homolog ical algebra.- R. Rivet: Anneaux de sries formelles et anneaux henseliens.- P. Salmon: Applicazioni della K-teoria allalgebra commutativa.- M. Tierney: Axiomatic sheaf theory: someconstructions and applications.- C.B. Winters: An elementary lecture on alg ebraic spaces |
Note: | Springer eBooks |
Contents: | L. Badescu: Sur certaines singularits des varits algbriques |
D.A. Buchsbaum: Homological and commutative algebra | |
S. Greco: Anelli Henseliani | |
C. Lair: Morphismes et structures algbriques | |
B.A. Mitchell: Introduction to category theory and homological algebra | |
R. Rivet: Anneaux de sries formelles et anneaux henseliens | |
P. Salmon: Applicazioni della K | |
teoria allalgebra commutativa | |
M. Tierney: Axiomatic sheaf theory: some constructions and applications | |
C.B. Winters: An elementary lecture on algebraic spaces | |
ISBN: | 9783642109799 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v58 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2011-9780857291608:ONLINE Show nearby items on shelf |
Title: | Representation Theory of the Virasoro Algebra [electronic resource] |
Author(s): |
Kenji Iohara Yoshiyuki Koga |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of theVirasoro algebra in a self- contained manner. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and the rational vertex operator algebrasassociated to the so-called minimal series represe ntations. Covering a wide range of material, this book has three appendices which provide background information required for some of the chapters. Fundamental resultsareorganizedin a unified way and existing proofs refined. For instance in chapter three, a generalization of Jantzen filtration is reformulated in an algebraic manner, and geometric interpretation is provided. Statements, widelybelieved to be true, are collated, and results which are known but not verified are proven, such as the corrected s tructure theorem of Fock modules in chapter eight. This book will be of interest to a wide range of mathematicians andphysicists from the level of graduate students to researchers |
Note: | Springer eBooks |
Contents: | Preliminary |
Classification of Harish | |
Chandra Modules | |
The Jantzen Filtration | |
Determinant Formulae | |
Verma Modules I: Preliminaries | |
Verma Modules II: Structure Theorem | |
A Duality among Verma Modules | |
Fock Modules | |
Rational Vertex Operator Algebras | |
Coset Constructions for sl2 | |
Unitarisable Harish | |
Chandra Modules | |
Homological Algebras | |
Lie p | |
algebras | |
Vertex Operator Algebras | |
ISBN: | 9780857291608 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Functions, special , Combinatorics |
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Call number: | SPRINGER-2011-9780857291066:ONLINE Show nearby items on shelf |
Title: | Monomial Ideals [electronic resource] |
Author(s): |
Jrgen Herzog Takayuki Hibi |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of researchspanning these fields , Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory of Grbner bases as well as the detailed study of generic initial ideals. Part II supplies Hilbert functions andresolutions and some of the combinatorics r elated to monomial ideals including the KruskalKatona theorem and algebraic aspects of Alexander duality. Part III discusses combinatorial applications of monomial ideals, providing avaluable overview of some of the central trends in algebraic combinatori cs. Main subjects include edge ideals of finite graphs, powers of ideals, algebraic shifting theory and an introduction to discrete polymatroids. Theory iscomplemented by a number of examples and exercises throughout, bringing the reader to a deeper under standing of concepts explored within the text. Self-contained and concise, this book will appeal to a wide range of readers, includingPhD students on advanced courses, experienced researchers, and combinatorialists and non-specialists with a basic knowled ge of commutative algebra. Since their first meeting in 1985, Juergen Herzog (Universitt Duisburg-Essen,Germany) and Takayuki Hibi (Osaka University, Japan), have worked together on a number of research projects, of which recent results are presented in t his monograph |
Note: | Springer eBooks |
Contents: | Part I Grbner bases: Monomial Ideals |
A short introduction to Grbner bases | |
Monomial orders and weights | |
Generic initial ideals | |
The exterior algebra | |
Part II: Hilbert functions and resolutions | |
Hilbert functions and the theorems of Macaulay and Kruskal | |
Katona | |
Resolutions of monomial ideals and the Eliahou | |
Kervaire formula | |
Alexander duality and resolutions | |
Part III Combinatorics: Alexander duality and finite graphs | |
Powers of monomial ideals | |
Shifting theory | |
Discrete Polymatroids | |
Some homological algebra | |
Geometry | |
ISBN: | 9780857291066 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v260 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2011-9780817647353:ONLINE Show nearby items on shelf |
Title: | Higher Structures in Geometry and Physics [electronic resource] : In Honor of Murray Gerstenhaber and Jim Stasheff |
Author(s): |
Alberto S Cattaneo Anthony Giaquinto Ping Xu |
Date: | 2011 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics such as algebra, algebraic topology, differentialgeometry, algebraic geome try, mathematical physics and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformationquantization, theory of algebroids and groupoids, symplec tic field theory, and much more. The ideas of higher homotopies and algebraic deformation have a growing number of theoretical applications and have played a prominent role inrecent mathematical advances. For example, algebraic versions of higher homotopi es have led eventually to the proof of the formality conjecture and the deformation quantization of Poisson manifolds. As observed in deformations anddeformation philosophy, a basic observation is that higher homotopy structures behave much better than st rict structures. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. Higher Structures in Geometryand Physics is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures. Contributors: L. Breen, A.S. Cattaneo, M. Cahen, V.A. Dolgushev, G. Felder, A. Giaquinto,S. Gutt, J. Huebschmann, T. Kadeishvili, H. Kajiura, B. Keller, Y. Kosmann-Schwarzbach, J.-L. Loday, S.A. Merkulov, D. Sternheimer, D.E. Tamarkin, C. Torossian, B.L. Tsygan, S. Waldmann, R.N. Umble |
Note: | Springer eBooks |
Contents: | Topics in Algebraic deformation theory |
Origins and breadth of the theory of higher homotopies | |
The deformation philosophy, quantization and noncommutative space | |
time structures | |
Differential geometry of Gerbes and differential forms | |
Symplectic connections of Ricci type and star products | |
Effective BatalinVilkovisky theories, equivariant configuration spaces and cyclic chains | |
Noncommutative calculus and the Gauss | |
Manin connection | |
The Lie algebra perturbation lemma | |
Twisting Elements in Homotopy G | |
algebras | |
Homological perturbation theory and homological mirror symmetry | |
ISBN: | 9780817647353 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v287 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , Topological Groups , Mathematical physics |
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Call number: | SPRINGER-2010-9783642133688:ONLINE Show nearby items on shelf |
Title: | The Use of Ultraproducts in Commutative Algebra [electronic resource] |
Author(s): |
Hans Schoutens |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make astrong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zerocharacteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants calledchromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra |
Note: | Springer eBooks |
Contents: | Ultraproducts and ?o? Theorem |
Flatness | |
Uniform Bounds | |
Tight Closure in Positive Characteristic | |
Tight Closure in Characteristic Zero. Affine Case | |
Tight Closure in Characteristic Zero. Local Case | |
Cataproducts | |
Protoproducts | |
Asymptotic Homological Conjectures in Mixed Characteristic | |
ISBN: | 9783642133688 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1999 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra |
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Call number: | SPRINGER-2010-9783642012877:ONLINE Show nearby items on shelf |
Title: | Involution [electronic resource] : The Formal Theory of Differential Equations and its Applications in Computer Algebra |
Author(s): |
Werner M Seiler |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic,homological and combinatorial i deas. It presents for the first time in book form the theory of Pommaret bases, a special kind of Grbner bases closely related to Koszul homology, and contains an extensive discussion of the existenceand uniqueness of solutions of formally well-posed init ial value problems and a novel presentation of Vessiot's dual version of the Cartan-Khler theory. Special emphasis is put on a constructive approach leading to effectivealgorithms |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Formal Geometry of Differential Equations | |
3 Involution I: Algebraic Theory | |
4 Completion to Involution | |
5 Structure Analysis of Polynomial Modules | |
6 Involution II: Homological Theory | |
7 Involution III: Differential Theory | |
8 The Size of the Formal Solution Space | |
9 Existence and Uniqueness of Solutions | |
10 Linear Differential Equations | |
A Miscellaneous | |
B Algebra | |
C Differential Geometry | |
References | |
Glossary | |
Index | |
ISBN: | 9783642012877 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algorithms and Computation in Mathematics, 1431-1550 : v24 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra Data processing , Algebra , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2010-9783034604369:ONLINE Show nearby items on shelf |
Title: | Homological Algebra of Semimodules and Semicontramodules [electronic resource] : Semi-infinite Homological Algebra of Associative Algebraic Structures |
Author(s): |
Leonid Positselski |
Date: | 2010 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph deals with semi-infinite homological algebra. Intended as the definitive treatment of the subject of semi-infinite homology and cohomology of associative algebraic structures, it also contains material on thesemi-infinite (co)homology of Lie algebras and topological groups, the derived comodule-contramodule correspondence, its application to the duality between representations of infinite-dimensional Lie algebras with complementary centralcharges, and relative non-homogeneous Koszul du ality. The book explains with great clarity what the associative version of semi-infinite cohomology is, why it exists, and for what kind of objects it is defined. Semialgebras,contramodules, exotic derived categories, Tate Lie algebras, algebraic Harish- Chandra pairs, and locally compact totally disconnected topological groups all interplay in the theories developed in this monograph. Contramodules,introduced originally by Eilenberg and Moore in the 1960s but almost forgotten for four decades, are featur ed prominently in this book, with many versions of them introduced and discussed. Rich in new ideas on homological algebra andthe theory of corings and their analogues, this book also makes a contribution to the foundational aspects of representation theo ry. In particular, it will be a valuable addition to the algebraic literature available to mathematicalphysicists |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
0 Preliminaries and Summary | |
1 Semialgebras and Semitensor Product | |
2 Derived Functor SemiTor | |
3 Semicontramodules and Semihomomorphisms | |
4 Derived Functor SemiExt | |
5 Comodule | |
Contramodule Correspondence | |
6 Semimodule | |
Semicontramodule Correspondence | |
7 Functoriality in the Coring | |
8 Functoriality in the Semialgebra | |
9 Closed Model Category Structures | |
10 A Construction of Semialgebras | |
11 Relative Nonhomogeneous Koszul Duality | |
Appendix A Contramodules over Coalgebras over Fields | |
Appendix B Comparison with Arkhipov's Ext^{\infty/2+*} and Se | |
ISBN: | 9783034604369 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monografie Matematyczne : v70 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry |
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Call number: | SPRINGER-2010-9783034602860:ONLINE Show nearby items on shelf |
Title: | Advances in Ring Theory [electronic resource] |
Author(s): |
Dinh Huynh Sergio R Lpez-Permouth |
Date: | 2010 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70thbirthday. The article s are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and itsgeneralizations, etc. Included are also applications of r ing theory to problems in coding theory and in linear algebra |
Note: | Springer eBooks |
Contents: | Foreward |
Biographical sketch of S.K. Jain | |
Applications of Cogalois theory to elementary field arithmetic | |
On big lattices of classes of R | |
modules defined by closure properties | |
Reversible and duo group rings | |
Principally quasi | |
Baer ring hulls | |
Strongly prime ideals of near | |
rings of continuous functions | |
Elements of minimal prime ideals in general rings | |
The Camps | |
Dicks theorem | |
Applications of the stone duality in the theory of precompact Boolean rings | |
Over rings and functors | |
On some classes of repeated | |
root constacyclic codes of length a power of 2 over Galois Rings | |
ISBN: | 9783034602860 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2010-9780817649340:ONLINE Show nearby items on shelf |
Title: | Cohomological and Geometric Approaches to Rationality Problems [electronic resource] : New Perspectives |
Author(s): |
Fedor Bogomolov Yuri Tschinkel |
Date: | 2010 |
Edition: | 1 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
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Note: | Rationality problems link algebra to geometry. The difficulties involved depend on the transcendence degree over the ground field, or geometrically, on the dimension of the variety. A major success in 19th century algebraicgeometry was a complete sol ution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. These advances have led to many interdisciplinary applications of algebraic geometry.This comprehensive text consists of surveys and research papers by leading specialists in the field. Topics discussed include the rationality of quotient spaces, cohomological invariants of finite groups of Lie type, rationality ofmoduli spaces of curves, and rational points on algebraic varieties. Th is volume is intended for research mathematicians and graduate students interested in algebraic geometry, and specifically in rationality problems. I. Bauer C.Bhning F. Bogomolov F. Catanese I. Cheltsov N. Hoffmann S.-J. Hu M.-C. Kang L. Katzarkov B. Kuny avskii A. Kuznetsov J. Park T. Petrov Yu. G. Prokhorov A.V. Pukhlikov Yu. Tschinkel |
Note: | Springer eBooks |
Contents: | The Rationality of Certain Moduli Spaces of Curves of Genus 3 |
The Rationality of the Moduli Space of Curves of Genus 3 after P. Katsylo | |
Unramified Cohomology of Finite Groups of Lie Type | |
Sextic Double Solids | |
Moduli Stacks of Vector Bundles on Curves and the KingSchofield Rationality Proof | |
Noethers Problem for Some | |
Groups | |
Generalized Homological Mirror Symmetry and Rationality Questions | |
The Bogomolov Multiplier of Finite Simple Groups | |
Derived Categories of Cubic Fourfolds | |
Fields of Invariants of Finite Linear Groups | |
The Rationality Problem and Birational Rig | |
ISBN: | 9780817649340 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v282 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , Topological Groups |
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Call number: | SPRINGER-2009-9783540858188:ONLINE Show nearby items on shelf |
Title: | Lower Central and Dimension Series of Groups [electronic resource] |
Author(s): |
Roman Mikhailov Inder Bir Singh Passi |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series, which consists of the subgroups determined by the augmentation powers, is a challengingtask. This monograph presents an exposition of different methods for investigating this relationship. In addition to group theorists, the results are also of interest to topologists and number theorists. The approach is mainlycombinatorial and homological. A novel feature is an exposition of simplicial methods for the study of problems in group theory |
Note: | Springer eBooks |
Contents: | Lower Central Series |
Dimension Subgroups | |
Derived Series | |
Augmentation Powers | |
Homotopical Aspects | |
Miscellanea | |
ISBN: | 9783540858188 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1952 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Algebraic topology |
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Call number: | SPRINGER-2009-9783540853329:ONLINE Show nearby items on shelf |
Title: | Generalized Lie Theory in Mathematics, Physics and Beyond [electronic resource] |
Author(s): |
Sergei Silvestrov Eugen Paal Viktor Abramov Alexander Stolin |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
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Note: | The goal of this book is to extend the understanding of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics. This volume is devoted to theinterplay between severa l rapidly expanding research fields in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensionsof differential calculus and geometry, non-ass ociative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book will be a useful source ofinspiration for a broad spectrum of researchers and for research students , and includes contributions from several large research communities in modern mathematics and physics. This volume consists of 5 parts comprising 25 chapters,which were contributed by 32 researchers from 12 different countries. All contributions in the v olume have been refereed |
Note: | Springer eBooks |
Contents: | Non |
Associative and Non | |
Commutative Structures for Physics | |
Moufang Transformations and Noether Currents | |
Weakly Nonassociative Algebras, Riccati and KP Hierarchies | |
Applications of Transvectants | |
Automorphisms of Finite Orthoalgebras, Exceptional Root Systems and Quantum Mechanics | |
A Rewriting Approach to Graph Invariants | |
Non | |
Commutative Deformations, Quantization, Homological Methods, and Representations | |
Graded q | |
Differential Algebra Approach to q | |
Connection | |
On Generalized N | |
Complexes Coming from Twisted Derivations | |
Remarks on Quantizations, Words and R | |
Matrices | |
Conn | |
ISBN: | 9783540853329 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Mathematical physics |
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Call number: | SPRINGER-2009-9783540680307:ONLINE Show nearby items on shelf |
Title: | Homological Mirror Symmetry [electronic resource] : New Developments and Perspectives |
Author(s): |
Karl-Georg Schlesinger Maximilian Kreuzer Anton Kapustin |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
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Note: | Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years. The present volume bridges a gap inthe literature by pro viding a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives. With contributions by K. Fukaya, M. Herbst, K. Hori, M. Huang, A.Kapustin, L. Katzarkov, A. Klemm, M. Konts evich, D. Page, S. Quackenbush, E. Sharpe, P. Seidel, I. Smith and Y. Soibelman, this volume will be a reference on the topic for everyone starting to work or actively working on mathematicalaspects of quantum field theory |
Note: | Springer eBooks |
Contents: | The Symplectic Geometry of Cotangent Bundles from a Categorical Viewpoint |
B | |
Type D | |
Branes in Toric CalabiYau Varieties | |
Topological String Theory on Compact CalabiYau: Modularity and Boundary Conditions | |
Gauge Theory, Mirror Symmetry, and the Geometric Langlands Program | |
Homological Mirror Symmetry and Algebraic Cycles | |
Notes on A | |
Algebras, A | |
Categories and Non | |
Commutative Geometry | |
On Non | |
Commutative Analytic Spaces Over Non | |
Archimedean Fields | |
Derived Categories and Stacks in Physics | |
ISBN: | 9783540680307 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v757 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Algebra , Mathematical physics |
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Call number: | SPRINGER-2009-9783034601894:ONLINE Show nearby items on shelf |
Title: | Simplicial Homotopy Theory [electronic resource] |
Author(s): |
Paul G Goerss John F Jardine |
Date: | 2009 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed modelcategory and, in particula r, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, includingalgebraic K-theory. This book supplies a modern e xposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups,Postnikov towers, and bisimplicial sets. The more advanced material in cludes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence.Interspersed throughout are many results and ideas well-known to experts, but uncollected in the lit erature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory.An extensive background in topology is not assumed. Reviews: a book filling an obvious gap in the literature and the au thors have done an excellent job on it. No monograph or expository paper has been published on this topic inthe last twenty-eight years. - Analele Universitatii din Timisoara is clearly presented and a brief summary preceding every chapter is useful to t he reader. The book should prove enlightening to a broad range of readersincluding prospective students and researchers who want to apply simplicial techniques for whatever reason. - Zentralblatt MATH they succeed. The book is an excellent account of sim plicial homotopy theory from a modern point ofview [] The book is well written. [] The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques |
Note: | Springer eBooks |
ISBN: | 9783034601894 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2009-9780817647438:ONLINE Show nearby items on shelf |
Title: | Riemannian Topology and Geometric Structures on Manifolds [electronic resource] |
Author(s): |
Krzysztof Galicki Santiago R Simanca |
Date: | 2009 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
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Note: | Springer 2013 e-book collections |
Note: | Riemannian Topology and Geometric Structures on Manifolds results from a similarly entitled conference held at the University of New Mexico in Albuquerque. The various contributions to this volume discuss recent advances in theareas of positive secti onal curvature, Khler and Sasaki geometry, and their interrelation to mathematical physics, notably M and superstring theory. Focusing on these fundamental ideas, this collection presents articles with originalresults, and plausible problems of interest f or future research. Contributors: C.P. Boyer, J. Cheeger, X. Dai, K. Galicki, P. Gauduchon, N. Hitchin, L. Katzarkov, J. Kollr, C. LeBrun, P. Rukimbira, S.R. Simanca, J. Sparks, C. vanCoevering, and W. Ziller |
Note: | Springer eBooks |
Contents: | Preface |
Charles P. BoyerAn Autobiographical Sketch | |
Charles P. BoyerList of Publications | |
Jeff Cheeger and Xianzhe Dai L2 | |
cohomology of non | |
isolated conical singularities and non | |
multiplicativity of the signature | |
Paul Gauduchon Hirzebruch surfaces and weighted projective planes | |
Nigel Hitchin Quaternionic Khler moduli spaces | |
Ludmil Katzarkov Homological mirror symmetry and Weyl tori | |
Jnos Kollr Positive Sasakian structures on 5 | |
manifolds | |
Claude LeBrun Four | |
manifolds, curvature bounds, and convex geometry | |
Phillipe Rukimbira The 1 | |
nullity of Sasakian manifolds | |
ISBN: | 9780817647438 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v271 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , Geometry , Mathematical physics |
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Call number: | SPRINGER-2009-9780387763569:ONLINE Show nearby items on shelf |
Title: | Polytopes, Rings, and K-Theory [electronic resource] |
Author(s): |
Joseph Gubeladze Winfried Bruns |
Date: | 2009 |
Edition: | 1 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, thealgebras derived from the m, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphismproblems and automorphism groups, homological prope rties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. Thismonograph has been written with a view towards graduate students and resear chers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, alsospecialists in lattice polytopes and related objects will find an up-to-date discussion of affine m onoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructiveapproach wherever possible. Winfried Bruns is Professor of Mathematics at Universitt Osnabrck. Joseph Gubeladze is Professor of Mathematics at San Francisco State University |
Note: | Springer eBooks |
Contents: | Preface |
Polytopes, cones, and complexes | |
Affine monoids and their Hilbert bases | |
Multiples of lattice polytopes | |
Monoid algebras | |
Isomorphisms and automorphisms | |
Homological properties and Hilbert functions | |
Grbner bases, triangulations, and Koszul algebras | |
Projective modules over monoid rings | |
Bass | |
Whitehead groups of monoid rings | |
Varieties | |
References | |
Notation | |
Index | |
ISBN: | 9780387763569 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , K-theory , Discrete groups |
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Call number: | SPRINGER-2009-9780387683249:ONLINE Show nearby items on shelf |
Title: | An Introduction to Homological Algebra [electronic resource] |
Author(s): |
Joseph J Rotman |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | With a wealth of examples as well as abundant applications to Algebra, this is a must-read work: a clearly written, easy-to-follow guide to Homological Algebra. The author provides a treatment of Homological Algebra whichapproaches the subject in ter ms of its origins in algebraic topology. In this brand new edition the text has been fully updated and revised throughout and new material on sheaves and abelian categories has been added. Applicationsinclude the following: * to rings -- Lazard's theorem that flat modules are direct limits of free modules, Hilbert's Syzygy Theorem, Quillen-Suslin's solution of Serre's problem about projectives over polynomial rings,Serre-Auslander-Buchsbaum characterization of regular local rings (and a sketch of unique f actorization) * to groups -- Schur-Zassenhaus, Gaschutz's theorem on outer automorphisms of finite p-groups, Schur multiplier, cotorsiongroups * to sheaves -- sheaf cohomology, Cech cohomology, discussion of Riemann-Roch Theorem over compact Riemann surfa ces. Learning Homological Algebra is a two-stage affair. Firstly, one must learn the language of Ext and Tor, andwhat this describes. Secondly, one must be able to compute these things using a separate language: that of spectral sequences. The basic prope rties of spectral sequences are developed using exact couples. All is done in the context ofbicomplexes, for almost all applications of spectral sequences involve indices. Applications include Grothendieck spectral sequences, change of rings, Lyndon-Hochs child-Serre sequence, and theorems of Leray and Cartan computing sheafcohomology. Joseph Rotman is Professor Emeritus of Mathematics at the University of Illinois at Urbana-Champaign. He is the author of numerous successful textbooks, including Advanced M odern Algebra (Prentice-Hall 2002), Galois Theory,2nd Edition (Springer 1998) A First Course in Abstract Algebra (Prentice-Hall 1996), Introduction to the Theory of Groups, 4th Edition (Springer 1995) |
Note: | Springer eBooks |
Contents: | Preface to the second edition |
How to read this book | |
Introduction | |
Hom and tensor | |
Special modules | |
Specific rings | |
Setting the stage | |
Homology | |
Tor and ext | |
Homology and rings | |
Homology and groups | |
Spectral sequences | |
References | |
Special notation | |
Index | |
ISBN: | 9780387683249 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2008-9783540735427:ONLINE Show nearby items on shelf |
Title: | A Singular Introduction to Commutative Algebra [electronic resource] |
Author(s): |
Gert-Martin Greuel Gerhard Pfister |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | From the reviews: It is certainly no exaggeration to say that Greuel and Pfister's A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra, in whichcomputational methods and r esults become central to how the subject is taught and learned. [] Among the great strengths and most distinctive features of Greuel and Pfister's book is a new, completely unified treatment of the globaland local theories. The realization that the two ca ses could be combined to this extent was decisive in the design of the Singular system, making it one of the most flexible and most efficient systems of its type. The authors presentthe first systematic development of this unified approach in a textbook h ere, and this aspect alone is almost worth the price of admission. Another distinctive feature of this book is the degree of integration of explicit computationalexamples into the flow of the text. Strictly mathematical components of the development (ofte n quite terse and written in a formal theorem-proof style) are interspersed with parallel discussions of features of Singular and numerousSingular examples giving input commands, some extended programs in the Singular language, and output. [] Yet another strength of Greuel and Pfister's book is its breadth of coverage of theoretical topics in the portions ofcommutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic. A synopsis of the table of contents will make th is clear. [] Greuel and Pfister have written a distinctive an highly useful bookthat should be in the library of every commutative algebrais and algebraic geometer, expert and novice alike. I hope that it achieves the educational impact it deserves. John B. Little, Monthly of The Mathematical Association ofAmerica, March 2004 ... The authors' most important new focus is the presentation of non-well orderings that allow them the computat |
Note: | Springer eBooks |
Contents: | Rings, Ideals and Standard Bases |
Modules | |
Noether Normalization and Applications | |
Primary Decomposition and Related Topics | |
Hilbert Function and Dimension | |
Complete Local Rings | |
Homological Algebra | |
ISBN: | 9783540735427 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra Data processing , Algebra , Geometry, algebraic , Computer science Mathematics , Algorithms |
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Call number: | SPRINGER-2008-9783540378891:ONLINE Show nearby items on shelf |
Title: | Cohomology of Number Fields [electronic resource] |
Author(s): |
Jrgen Neukirch Alexander Schmidt Kay Wingberg |
Date: | 2008 |
Edition: | Second Edition |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. The first part providesalgebraic background: coho mology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galoisgroups of local and global fields: Tate duality , structure of absolute Galois groups of local fields, extensions with restricted ramification, Poitou-Tate duality, Hasse principles, theorem of Grunwald-Wang, Leopoldts conjecture,Riemanns existence theorem, the theorems of Iwasawa and of afarevic on so lvable groups as Galois groups, Iwasawa theory, and anabelian principles. New material is introduced here on duality theorems for unramified and tamelyramified extensions, a careful analysis of 2-extensions of real number fields and a complete proof of Ne ukirchs theorem on solvable Galois groups with given local conditions. The present edition is a corrected printing of the 2008edition |
Note: | Springer eBooks |
Contents: | Part I Algebraic Theory: Cohomology of Profinite Groups |
Some Homological Algebra | |
Duality Properties of Profinite Groups | |
Free Products of Profinite Groups | |
Iwasawa Modules | |
Part II Arithmetic Theory: Galois Cohomology | |
Cohomology of Local Fields | |
Cohomology of Global Fields | |
The Absolute Galois Group of a Global Field | |
Restricted Ramification | |
Iwasawa Theory of Number Fields | |
Anabelian Geometry | |
Literature | |
Index | |
ISBN: | 9783540378891 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v323 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , Number theory |
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Call number: | SPRINGER-2008-9780387746142:ONLINE Show nearby items on shelf |
Title: | Topological Methods in Group Theory [electronic resource] |
Author(s): |
Ross Geoghegan |
Date: | 2008 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Topological Methods in Group Theory is about the interplay between algebraic topology and the theory of infinite discrete groups. The author has kept three kinds of readers in mind: graduate students who have had an introductorycourse in algebraic to pology and who need a bridge from common knowledge to the current research literature in geometric, combinatorial and homological group theory group theorists who would like to know more about the topologicalside of their subject but who have been too lon g away from topology and manifold topologists, both high- and low-dimensional, since the book contains much basic material on proper homotopy and locally finite homology not easily foundelsewhere. The book focuses on two main themes: 1. Topological Finite ness Properties of groups (generalizing the classical notions of finitely generated and finitely presented) 2. Asymptotic Aspects of Infinite Groups(generalizing the classical notion of the number of ends of a group). Illustrative examples treated in some detail include: Bass-Serre theory, Coxeter groups, Thompson groups, Whitehead's contractible 3-manifold, Davis's exoticcontractible manifolds in dimensions greater than three, the Bestvina-Brady Theorem, and the Bieri-Neumann-Strebel invariant. The book also includes a highly geometrical treatment of Poincar duality (via cells and dual cells) tobring out the topological meaning of Poincar duality groups. To keep the length reasonable and the focus clear, it is assumed that the reader knows or can easily learn the necessary algebra (which is clearly summarized) but wants tosee the topology done in detail. Apart from the introductory material, most of the mathematics presented here has not appeared in book form before |
Note: | Springer eBooks |
Contents: | Preface |
CW Complexes and Homotopy | |
Cellular Homology | |
Fundamental Group and Tietze Transformations | |
Some Techniques In Homotopy Theory | |
Elementary Geometric Topology | |
The Borel Construction and Bass | |
Serre Theory | |
Topological Finiteness Properties and Dimension of Groups | |
Homological Finitenes Properties of Groups | |
Finiteness Properties of Some Important Groups | |
Locally Finite CW Complexes and Proper Homotopy | |
Locally Finite Homology | |
Cohomology of CW Complexes | |
Cohomology of Groups and Ends of Covering Spaces | |
Filtered Ends of Pairs of Groups | |
Poincare Duality in | |
ISBN: | 9780387746142 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v243 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Topological Groups , Topology |
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Call number: | SPRINGER-2008-9780387685489:ONLINE Show nearby items on shelf |
Title: | Braid Groups [electronic resource] |
Author(s): |
Christian Kassel Vladimir Turaev |
Date: | 2008 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory ofbraids stems from their at tractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authorsthoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braidgroups, the Alexander--Conway and Jones link polynomials, connections wit h the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups. This book will serve graduatestudents, mathematicians, and theoretical physicists interested in low-dimensional topology and its co nnections with representation theory |
Note: | Springer eBooks |
Contents: | Braids and Braid Groups |
Braids, Knots, and Links | |
Homological Representations of the Braid Groups | |
Symmetric Groups and IwahoriHecke Algebras | |
Representations of the IwahoriHecke Algebras | |
Garside Monoids and Braid Monoids | |
An Order on the Braid Groups | |
Presentations of SL(Z) and PSL(Z) | |
Fibrations and Homotopy Sequences | |
The BirmanMurakamiWenzl Algebras | |
Left Self | |
Distributive Sets | |
ISBN: | 9780387685489 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v247 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Algebra , Algebraic topology , Cell aggregation Mathematics |
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Call number: | SPRINGER-2007-9783834895011:ONLINE Show nearby items on shelf |
Title: | Lectures on Algebraic Geometry I [electronic resource] : Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces |
Author(s): |
Gnter Harder |
Date: | 2007 |
Publisher: | Wiesbaden : Vieweg+Teubner |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods areindispensable for modern alge braic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compactRiemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them |
Note: | Springer eBooks |
ISBN: | 9783834895011 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry |
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Call number: | SPRINGER-2007-9783764375249:ONLINE Show nearby items on shelf |
Title: | Tool and Object [electronic resource] : A History and Philosophy of Category Theory |
Author(s): |
Ralf Krmer |
Date: | 2007 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book is first of all a history of category theory from the beginnings to A. Grothendieck and F.W. Lawvere. Category theory was an important conceptual tool in 20th century mathematics whose influence on some mathematicalsubdisciplines (above all algebraic topology and algebraic geometry) is analyzed. Category theory also has an important philosophical aspect: on the one hand its set-theoretical foundation is less obvious than for other mathematicaltheories, and on the other hand it unifies concep tually a large part of modern mathematics and may therefore be considered as somewhat fundamental itself. The role of this philosophical aspect in the historical development is thesecond focus of the book. Relying on the historical analysis, the author de velops a philosophical interpretation of the theory of his own, intending to get closer to how mathematicians conceive the significance of their activity thantraditional schools of philosophy of science. The book is the first monography exclusively devote d to the history of category theory. To a substantial extent it considers aspects never studied before. The author uses (and justifies theuse of) a methodology combining historical and philosophical approaches. The analysis is not confined to general rema rks, but goes into considerable mathematical detail. Hence, the book provides an exceptionally thorough case studycompared with other works on history or philosophy of mathematics. The philosophical position developed here (inspired by Peircean pragmatism and Wittgenstein) is an interesting alternative to traditional approaches in philosophy ofmathematics like platonism, formalism and intuitionism |
Note: | Springer eBooks |
Contents: | Prelude: Poincar, Wittgenstein, Peirce, and the use of concepts |
Category theory in Algebraic Topology | |
Category theory in Homological Algebra | |
Category theory in Algebraic Geometry | |
From tool to object: full | |
fledged category theory | |
Categories as sets: problems and solutions | |
Categorial foundations | |
Pragmatism and category theory | |
ISBN: | 9783764375249 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Science Networks. Historical Studies : v32 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Mathematics_$xHistory |
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Call number: | SPRINGER-2007-9780817646134:ONLINE Show nearby items on shelf |
Title: | Advanced Algebra [electronic resource] : Along with a companion volume Basic Algebra |
Author(s): |
Anthony W Knapp |
Date: | 2007 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a globalview of algebra and its r ole in mathematics as a whole. Key topics and features of Advanced Algebra: *Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementarytheory of modules as developed in Basic Algebra *Ch apters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, andalgebraic geometry *Sections in two chapters relate the theory to the su bject of Grbner bases, the foundation for handling systems of polynomial equations in computer applications *Text emphasizes connections between algebra andother branches of mathematics, particularly topology and complex analysis *Book carries on two prom inent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationshipbetween number theory and geometry *Many examples and hundreds of problems are included, along with hints or complete s olutions for most of the problems *The exposition proceeds from the particular to the general, often providingexamples well before a theory that incorporates them it includes blocks of problems that illuminate aspects of the text and introduce additional topics Advanced Algebra presents its subject matter in a forward-looking way that takesinto account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topicsdeveloped in Basic Algebra |
Note: | Springer eBooks |
Contents: | Transition to Modern Number Theory |
WedderburnArtin Ring Theory | |
Brauer Group | |
Homological Algebra | |
Three Theorems in Algebraic Number Theory | |
Reinterpretation with Adeles and Ideles | |
Infinite Field Extensions | |
Background for Algebraic Geometry | |
The Number Theory of Algebraic Curves | |
Methods of Algebraic Geometry | |
ISBN: | 9780817646134 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Cornerstones |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic , Field theory (Physics) , Number theory |
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Call number: | SPRINGER-2007-9780817645748:ONLINE Show nearby items on shelf |
Title: | The Grothendieck Festschrift [electronic resource] A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck |
Author(s): |
Pierre Cartier Luc Illusie Nicholas M Katz Grard Laumon Yuri I Manin Kenneth A Ribet |
Date: | 2007 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The many diverse articles presented in these three volumes, collected on the occasion of Alexander Grothendiecks sixtieth birthday and originally published in 1990, were offered as a tribute to one of the worlds greatestliving mathematicians. Grothen dieck changed the very way we think about many branches of mathematics. Many of his ideas, revolutionary when introduced, now seem so natural as to have been inevitable. Indeed, it is difficult to fullygrasp the influence his vast contributions to modern mathematics have subsequently had on new generations of mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundationalto the subject. Topics addressed by these top-notch contributors match th e breadth of Grothendiecks own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory,K-theory, category theory, and homological algebra. CONTRIBUTORS to Volume I: A. Altman M. Artin V. Bala ji A. Beauville A.A. Beilinson P. Berthelot J.-M. Bismut S. Bloch L. Breen J.-L. Brylinski J. Dieudonn H. Gillet A.B.Goncharov K. Kato S. Kleiman W. Messing V.V. Schechtman C.S. Seshadri C. Soul J. Tate M. van den Bergh and A.N. Varchenko |
Note: | Springer eBooks |
Contents: | Foreword |
Bibliographie d'Alexander Grothendieck | |
Dieudonne | |
Altman and Kleiman | |
Artin, Tate, and van den Bergh | |
Balaji and Seshadri | |
Beauville | |
Beilinson, Goncharov, Schechtman, and Varchenko | |
Berthelot and Messing | |
Bismut, Gillet, and Soule | |
Bloch and Kato | |
Breen | |
Brylinski | |
ISBN: | 9780817645748 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , K-theory , Functional analysis , Number theory , Algebraic topology |
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Call number: | SPRINGER-2007-9780387488998:ONLINE Show nearby items on shelf |
Title: | Exercises in Modules and Rings [electronic resource] |
Author(s): |
T. Y Lam |
Date: | 2007 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | For the Backcover This Problem Book offers a compendium of 639 exercises of varying degrees of difficulty in the subject of modules and rings at the graduate level. The material covered includes projective, injective, and flatmodules, homological and uniform dimensions, noncommutative localizations and Goldies theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, as well as Moritas classical theory of category dualities andequivalences. Each of the nineteen sections begins with a n introduction giving the general background and the theoretical basis for the problems that follow. All exercises are solved in full detail many are accompanied by pertinenthistorical and bibliographical information, or a commentary on possible improveme nts, generalizations, and latent connections to other problems. This volume is designed as a problem book for the authors Lectures on Modules and Rings(Springer GTM, Vol. 189), from which the majority of the exercises were taken. Some forty new exercises have been added to further broaden the coverage. As a result, this book is ideal both as a companion volume to Lectures, and as asource for independent study. For students and researchers alike, this book will also serve as a handy reference for a copious amount of information in algebra and ring theory otherwise unavailable from textbooks. An outgrowth of theauthors lecture courses and seminars over the years at the University of California at Berkeley, this book and its predecessor Exercises in Classica l Ring Theory (Springer, 2003) offer to the mathematics community the fullest andmost comprehensive reference to date for problem solving in the theory of modules and rings |
Note: | Springer eBooks |
Contents: | Free Modules |
Projective and Injective Modules | |
Flat Modules and Homological Dimensions | |
More Theory of Modules | |
Rings of Quotients | |
More Rings of Quotients | |
robenius and Quasi | |
Frobenius Rings | |
Matrix Rings, Categories of Modules, and Morita Theory | |
ISBN: | 9780387488998 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Problem Books in Mathematics, 0941-3502 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2006-9783540337911:ONLINE Show nearby items on shelf |
Title: | Mathematical Survey Lectures 19432004 [electronic resource] |
Author(s): |
Beno Eckmann |
Date: | 2006 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This collection traces the career of Beno Eckmann, whose work ranges across a broad spectrum of mathematical concepts from topology and differential geometry through homological algebra to group theory. One of our most influentialliving mathematician s, Eckmann has been associated for nearly his entire professional life with the Swiss Federal Institute of Technology Zurich (ETH), as student, lecturer, professor, and professor emeritus. The lectures offer afascinating account of advances in pure mathem atics from 1943 to 2004, as new topics and methods are introduced, and gradually become routine. The penultimate lecture is a personal-historical overview of algebraic topology, deliveredin connection with the 40-year jubilee of the Institute for Mathemat ical Research (FIM), which Eckmann founded at ETH in 1964. In the final article, Eckmann looks beyond pure mathematics to consider the application in concrete fieldsof intellectual enterprise |
Note: | Springer eBooks |
Contents: | Lide de dimension (1943) |
Topology and Algebra (1943) | |
Complex | |
analytic manifolds (1950) | |
Homotopie et dualit (1956) | |
Groupes dhomotopie et dualit (1958) | |
Homotopy and Cohomology Theory (1962) | |
Simple Homotopy Type and Categories of Fractions (1970) | |
Some Recent Developments in the Homology Theory of Groups (1980) | |
Poincar Duality Groups of Dimension 2 are Surface Groups (1986) | |
Continuous Solutions of Linear Equations (1991) | |
Mathematics: Questions and Answers (1994) | |
Hurwitz | |
Radon Matrices Revisited (1994) | |
Birth of Fibre Spaces, and Homotopy (1996) | |
4 | |
ISBN: | 9783540337911 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Global differential geometry , Algebraic topology |
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Call number: | SPRINGER-2006-9783540279914:ONLINE Show nearby items on shelf |
Title: | Idempotent Matrices over Complex Group Algebras [electronic resource] |
Author(s): |
Ioannis Emmanouil |
Date: | 2006 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The theory of idempotent matrices with entries in complex group algebras has recently experienced a revival, in view of its close relationship with deep geometric problems and conjectures. The relevant questions studied in thisbook for general groups are motivated by specific examples. A variety of techniques is employed from commutative algebra, homological algebra and functional analysis. The book can serve as an introduction to this lively research area.The pace is suitable for independent study a nd the level of the presentation not very demanding. The exercises at the end of each chapter form an essential part of the book |
Note: | Springer eBooks |
Contents: | Introduction |
Motivating Examples | |
Reduction to Positive Characteristic | |
A Homological Approach | |
Completions of CG | |
Appendices: Tools from Commutative Algebra | |
Discrete Ring | |
valued Integrals | |
Frobenius' Density Theorem | |
Homological Techniques | |
Comparison of Projections | |
ISBN: | 9783540279914 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , K-theory , Functional analysis |
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Call number: | SPRINGER-2006-9783540279501:ONLINE Show nearby items on shelf |
Title: | Categories and Sheaves [electronic resource] |
Author(s): |
Masaki Kashiwara Pierre Schapira |
Date: | 2006 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays. This book covers categories, homological algebraand sheaves in a system atic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond. The authors present the general theory ofcategories and functors, emphasising inductive a nd projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories andalso unbounded derived categories using transfinite induction and ac cessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies |
Note: | Springer eBooks |
Contents: | The Language of Categories |
Limits | |
Filtrant Limits | |
Tensor Categories | |
Generators and Representability | |
Indization of Categories | |
Localization | |
Additive and Abelian Categories | |
? | |
accessible Objects and F | |
injective Objects | |
Triangulated Categories | |
Complexes in Additive Categories | |
Complexes in Abelian Categories | |
Derived Categories | |
Unbounded Derived Categories | |
Indization and Derivation of Abelian Categories | |
Grothendieck Topologies | |
Sheaves on Grothendieck Topologies | |
Abelian Sheaves | |
Stacks and Twisted Sheaves | |
ISBN: | 9783540279501 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v332 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Cell aggregation Mathematics |
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Call number: | SPRINGER-2005-9783540263708:ONLINE Show nearby items on shelf |
Title: | Ideals and Reality [electronic resource] : Projective Modules and Number of Generators of Ideals |
Author(s): |
Friedrich Ischebeck Ravi A Rao |
Date: | 2005 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph tells the story of a philosophy of J-P. Serre and his vision of relating that philosophy to problems in affine algebraic geometry. It gives a lucid presentation of the Quillen-Suslin theorem settling Serre'sconjecture. The central topi c of the book is the question of whether a curve in $n$-space is as a set an intersection of $(n-1)$ hypersurfaces, depicted by the central theorems of Ferrand, Szpiro, Cowsik-Nori, Mohan Kumar, Boratnski.The book gives a comprehensive introduction to bas ic commutative algebra, together with the related methods from homological algebra, which will enable students who know only the fundamentals of algebra to enjoy the power of usingthese tools. At the same time, it also serves as a valuable reference for t he research specialist and as potential course material, because the authors present, for the first time in book form, an approach here that is an intermix ofclassical algebraic K-theory and complete intersection techniques, making connections with the fa mous results of Forster-Swan and Eisenbud-Evans. A study of projective modules and their connections with topological vector bundles in aform due to Vaserstein is included. Important subsidiary results appear in the copious exercises. Even this advanced m aterial, presented comprehensively, keeps in mind the young student as potential reader besides the specialists ofthe subject |
Note: | Springer eBooks |
ISBN: | 9783540263708 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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