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SPIRES-BOOKS: FIND KEYWORD GROUP THEORY AND GENERALIZATIONS *END*INIT* use /tmp/qspiwww.webspi1/15770.28 QRY 131.225.70.96 . find keyword group theory and generalizations ( in books using www Cover
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Call number:9783319452418:ONLINE Show nearby items on shelf
Title:A Group Theoretic Approach to Quantum Information
Author(s): Masahito Hayashi
Date:2017
Size:1 online resource (XIII, 228 p. 32 illus p.)
Contents:Foundation of Quantum Theory -- Quantum Channel, Information Quantities, and Their Mathematical Structure -- Quantum Entanglement and Its Quantification -- Group Covariance and Optimal Information Processing -- Quantum Error
Correcting Code and Its Application -- Universal Information Processings
ISBN:9783319452418
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Physics , Group theory , Quantum computers , Quantum physics , Spintronics , System safety , Physics , Quantum Physics , Quantum Information Technology, Spintronics , Quantum Computing , Group Theory and Generalizations , Security Science and Technology
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Call number:9783319449067:ONLINE Show nearby items on shelf
Title:Group Representation for Quantum Theory
Author(s): Masahito Hayashi
Date:2017
Size:1 online resource (XXVIII, 338 p. 54 illus., 1 illus. in color p.)
Contents:Foundation of Quantum Theory -- Group Representation -- Representations of Lie Group and Lie Algebra (Basics) -- Representations of Lie Group and Lie Algebra (Special Case) -- Representations of Lie Group and Lie Algebra (General
Case) -- Bosonic System -- Discretization of Bosonic System
ISBN:9783319449067
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Physics , Group theory , Quantum computers , Mathematical physics , Quantum physics , Spintronics , Physics , Quantum Physics , Group Theory and Generalizations , Quantum Information Technology, Spintronics , Quantum Computing , Mathematical Physics
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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-2016-9783319388557:ONLINE Show nearby items on shelf
Title:Multiplicative Ideal Theory and Factorization Theory Commutative and Non-commutative Perspectives
Author(s):
Date:2016
Size:1 online resource (407 p.)
Note:10.1007/978-3-319-38855-7
Contents:Multiplicative Ideal Theory in Non-commutative Rings (E. Akalan, H. Marubayashi) -- About number fields with Pólya group of order ≤ 2 (D. Adam, J.-L. Chabert) -- The interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmet ic Combinatorics (K. Cziczler, M. Domokos, A. Geroldinger) -- Ring and semigroup constructions (M. D'Anna) -- New Distinguished Classes of Spectral Spaces (C.A. Finocchiaro, M. Fontana, D. Spirito) -- Relative polynomial closure and monadically Krull mono ids of integer-valued polynomials (S. Frisch).-An overview of the computational aspects of nonunique factorization invariants (P.A. García-Sánchez).-Arithmetic of Mori domains and monoids: The global case (F. Kainrath) -- Prüfer Domains of Integer-Valu ed Polynomials (K.A. Loper, M. Syvuk) -- Lobal Properties of Integral Domains (T.G. Lucas) -- Topological aspects of irredundant intersections of ideals and valuation rings (B. Olberding) -- Noetherian semigroup algebras and beyond (J. Okniński)
-- Idempotent pairs and PRINC domains (G. Peruginelli, L. Salce, P. Zanardo) -- Some recent results and open problems on sets of lengths of Krull monoids with finite class group (W.A. Schmid) -- Factorizations of elements in noncommutative rings: A survey (D. Smertnig)
ISBN:9783319388557
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Proceedings in Mathematics & Statistics: 170
Keywords: Mathematics , Algebraic geometry , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Group theory , Number theory , Mathematics , Commutative Rings and Algebras , Number Theory , Group Theory and Generalizations , Associative Rings and Algebras , Algebraic Geometry
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Call number:SPRINGER-2016-9783319317564:ONLINE Show nearby items on shelf
Title:Geometric Methods in Physics XXXIV Workshop, Białowieża, Poland, June 28 – July 4, 2015
Author(s):
Date:2016
Size:1 online resource (20 p.)
Note:10.1007/978-3-319-31756-4
ISBN:9783319317564
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Group theory , Global analysis (Mathematics) , Manifolds (Mathematics) , Physics , Mathematics , Group Theory and Generalizations , Global Analysis and Analysis on Manifolds , Mathematical Methods in Physics
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Call number:SPRINGER-2016-9783319313382:ONLINE Show nearby items on shelf
Title:Essays in Mathematics and its Applications In Honor of Vladimir Arnold
Author(s):
Date:2016
Size:1 online resource (22 p.)
Note:10.1007/978-3-319-31338-2
Contents:A new way to compute the Rodrigues coefficients of functions of the Lie groups of matrices (D. Andrica, O.L. Chender) -- Quasimodes in integrable systems and semi-classical limit (M. Baldo, F. Raciti) -- Manifolds which are complex and symplectic bu t not Kahler (G. Bazzoni, V. Munoz) -- Solvability of a non clamped frictional contact problem with adhesion (O. Chau, D. Goeleven, R. Oujja) -- The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence (A. Fortunati, S. Wi ggins) -- Iterative Methods for the Elastography Inverse Problem of Locating Tumors (B. Jadamba, A.A. Khan, F. Raciti, C. Tammer, B. Winkler) -- Transversality theory with applications to differential equations (D. Motreanu, V.V. Motreanu) -- Lattice-like subsets of Euclidean Jordan algebras (A.B. Nemeth, S.Z. Nemeth) -- Simultaneous Diophantine approximation: Searching for analogues of Hurwitz’ theorem (W.G. Nowak) -- On the fixed points of a Hamiltonian diffeomorphism in presence of
fundamental group (K. Ono, A. Pajitnov) -- Some Generalizations of Fixed Point Theorems on S-Metric Spaces (N.Y. Ozgur, N.A. Tas) -- Functional Inequalities in Banach Spaces and Fuzzy Banach Spaces (C. Park, J.R. Lee, T.M. Rassias) -- The Maslov Ind ex in PDEs Geometry (A. Prastaro) -- On the infimum of certain functionals (B. Ricceri) -- The Algebra of Gyrogroups: Cayley Theorem, Lagrange Theorem, and Isomorphism Theorems (T. Suksumran) -- Mild continuity properties of relations and relators in rela tor spaces (A. Szaz, A. Zakaria) -- Contraction Maps in Pseudometric Structures (M. Turinici) -- Novel Tools to Determine Hyperbolic Triangle Centers (A.A. Ungar)
ISBN:9783319313382
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Dynamics , Ergodic theory , Global analysis (Mathematics) , Manifolds (Mathematics) , Algebraic topology , Complex manifolds , Mathematics , Dynamical Systems and Ergodic Theory , Algebraic Topology , Manifolds and Cell Complexes (incl. Diff.Topology) , Global Analysis and Analysis on Manifolds
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Call number:SPRINGER-2016-9783319281063:ONLINE Show nearby items on shelf
Title:University of Toronto Mathematics Competition (2001–2015)
Author(s): Edward J Barbeau
Date:2016
Size:1 online resource (1 p.)
Note:10.1007/978-3-319-28106-3
Contents:Preface -- 1. Problems of the Contests -- 2. Algebra -- 3. Inequalities -- 4. Sequences and Series -- 5. Calculus and its Applications -- 6. Other Topics in Analysis -- 7. Linear Algebra -- 8. Geometry -- 9. Group Theory -- 10. Combinatorics and Fi nite Mathematics -- 11. Number Theory -- Appendix A: Definitions, Conventions, Notation, and Basics -- Appendix B: Top-Ranking Students -- Index.
ISBN:9783319281063
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Group theory , Differential equations , Functions of real variables , Geometry , Mathematics , Real Functions , Geometry , Group Theory and Generalizations , Ordinary Differential Equations
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Call number:SPRINGER-2016-9783319247113:ONLINE Show nearby items on shelf
Title:Dessins d'Enfants on Riemann Surfaces
Author(s): Gareth A Jones
Date:2016
Edition:1st ed. 2016
Size:1 online resource (259 p.)
Note:10.1007/978-3-319-24711-3
Contents:Historical and introductory background -- Graph embeddings -- Dessins and triangle groups -- Galois actions -- Quasiplatonic surfaces, and automorphisms -- Regular maps -- Regular embeddings of complete graphs -- Wilson operations -- Further exampl es -- Arithmetic aspects -- Beauville surfaces
ISBN:9783319247113
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebraic geometry , Group theory , Functions of complex variables , Hyperbolic geometry , Mathematics , Algebraic Geometry , Group Theory and Generalizations , Functions of a Complex Variable , Several Complex Variables and Analytic Spaces , Hyperbolic Geometry
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Call number:SPRINGER-2014-9789400776425:ONLINE Show nearby items on shelf
Title:Symmetries in Fundamental Physics [electronic resource]
Author(s): Kurt Sundermeyer
Date:2014
Publisher:Dordrecht : Springer Netherlands : Imprint: Springer
Size:1 online resource
Note:Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the laws of nature areinvariant under spacetime tran sformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognitionfor nearly half a century, but can today be unders tood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, asshown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner ... if we knew all the laws of nature, or the ultimate Law of nature, the invarianceproperties of these laws would not furnish us new information. Thanks to Wigner we now also under stand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic propertiesof particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N. Yang and R. Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementaryparticle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry. The treatment of symmetries inthis monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity
Contents:Preface
Notation
Introduction
Symmetry: Argument, Principle, and Leitmotif
Operations and Invariants
Symmetries in Fundamental Physics
The Scope of Symmetries
Bibliographical Notes
Classical Mechanics
Newtonian and Analytical Mechanics
Symmetries and Conservation Laws
Galilei Group
Electrodynamics and Special Relativity
Electrodynamics la Maxwell
Special Relativity
Noether Theorems
Poincar Transformations
Generalizations of Poincar Symmetry
On the Validity of Special Relativity
Quantum Mechanics
Principles of Quantum Mechan
ISBN:9789400776425
Series:eBooks
Series:SpringerLink
Series:Fundamental Theories of Physics : v176
Series:Physics and Astronomy (Springer-11651)
Keywords: Quantum theory
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Call number:SPRINGER-2014-9783319065816:ONLINE Show nearby items on shelf
Title:Symmetries in Fundamental Physics [electronic resource]
Author(s): Kurt Sundermeyer
Date:2014
Edition:2nd ed. 2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the laws of nature areinvariant under spacetime tran sformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognitionfor nearly half a century, but can today be unders tood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, asshown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P.Wigner ... if we knew all the laws of nature, or the ultimate Law of nature, the invarianceproperties of these laws would not furnish us new information. Thanks to Wigner we now also unders tand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic propertiesof particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N.Yang and R. Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particlephysics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree mot ivated and inspired by considerations of symmetry.The treatment of symmetries in thismonograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity
Contents:Preface
Notation
Introduction
Symmetry: Argument, Principle, and Leitmotif
Operations and Invariants
Symmetries in Fundamental Physics
The Scope of Symmetries
Bibliographical Notes
Classical Mechanics
Newtonian and Analytical Mechanics
Symmetries and Conservation Laws
Galilei Group
Electrodynamics and Special Relativity
Electrodynamics la Maxwell
Special Relativity
Noether Theorems
Poincar Transformations
Generalizations of Poincar Symmetry
On the Validity of Special Relativity
Quantum Mechanics
Principles of Quantum Mechan
ISBN:9783319065816
Series:eBooks
Series:SpringerLink
Series:Fundamental Theories of Physics : v176
Series:Physics and Astronomy (Springer-11651)
Keywords: Quantum theory
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Call number:SPRINGER-2014-9783319021324:ONLINE Show nearby items on shelf
Title:Geometric Control Theory and Sub-Riemannian Geometry [electronic resource]
Author(s): Gianna Stefani
Ugo Boscain
Jean-Paul Gauthier
Andrey Sarychev
Mario Sigalotti
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry.On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language forstudying controllability, mot ion planning,stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand,Riemannian geometry and its generalizations, such a s sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to importantresults regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannianstructures, regularity of the Hausdorff volume
Contents:1 A. A. Agrachev
Some open problems
2 D. Barilari, A. Lerario
Geometry of Maslov cycles
3 Y. Baryshnikov, B. Shapiro
How to Run a Centipede: a Topological Perspective
4 B. Bonnard, O. Cots, L. Jassionnesse
Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces
5 J
B. Caillau, C. Royer
On the injectivity and nonfocal domains of the ellipsoid of revolution
6 P. Cannarsa, R. Guglielmi
Null controllability in large time for the parabolic Grushin operator with singular potential
7 Y. Chitour, M. Godoy Molina, P. Kokkonen
The rolli
ISBN:9783319021324
Series:eBooks
Series:SpringerLink
Series:Springer INdAM Series, 2281-518X : v5
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Mathematical optimization
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Call number:SPRINGER-2014-9781461485353:ONLINE Show nearby items on shelf
Title:Coherent States, Wavelets, and Their Generalizations [electronic resource]
Author(s): Syed Twareque Ali
Jean-Pierre Antoine
Jean-Pierre Gazeau
Date:2014
Edition:2nd ed. 2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) andvarious generalizations o f wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherentstates, wavelets, and some of their generaliz ations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take aclassical-like view of quantum states in physics. Starting from the standar d theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are squareintegrable over a homogeneous space a further step allows one to dispense with the group context altog ether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensionalwavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups,Gazeau-Klauder coherent states,coherent states forthe relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potentialapplications, from the quantum physicallyoriented,likethe quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing. Intended as an introduction to current research forgraduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the research liter
Contents:Canonical Coherent States
Positive Operator
Valued Measures and Frames
Some Group Theory
Hilbert Spaces
Square Integrable and Holomorphic Kernels
Covariant Coherent States
Coherent States from Square Integrable Representations
Some Examples and Generalizations
CS of General Semidirect Product Groups
CS of Product Groups
CS Quantizations and Probabilistic Aspects
Direct Wavelet Transforms
Multidimensional Wavelets
Wavelets Related to Other G Groups
The Discretization Problem
Frames Sampling and All That
ISBN:9781461485353
Series:eBooks
Series:SpringerLink
Series:Theoretical and Mathematical Physics, 1864-5879
Series:Physics and Astronomy (Springer-11651)
Keywords: Group theory , Quantum theory
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Call number:SPRINGER-2013-9780387927169:ONLINE Show nearby items on shelf
Title:Extensions of Rings and Modules [electronic resource]
Author(s): Gary F Birkenmeier
Jae Keol Park
S Tariq Rizvi
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:The focus of this monograph is the study of rings and modules which have a rich supply of direct summands with respect to various extensions. The first four chapters of the book discuss rings and modules which generalizeinjectivity (e.g., extending m odules), or for which certain annihilators become direct summands (e.g., Baer rings). Ring extensions such as matrix, polynomial, group ring, and essential extensions of rings from the aforementionedclasses are considered in the next three chapters. A the ory of ring and module hulls relative to a specific class of rings or modules is introduced and developed in the following two chapters. While applications of the resultspresented can be found throughout the book, the final chapter mainly consists of appl ications to algebra and functional analysis. These include obtaining characterizations of rings of quotients as direct products of prime rings anddescriptions of certain C*-algebras via (quasi-)Baer rings. Extensions of Rings and Modules introduces for th e first time in book form: * Baer, quasi-Baer, and Rickart modules * The theory of generalized triangular matrix rings viasets of triangulating idempotents * A discussion of essential overrings that are not rings of quotients of a base ring and Osofsky's study on the self-injectivity of the injective hull of a ring * Applications of the theory ofquasi-Baer rings to C*-algebras Each section of the book is enriched with examples and exercises which make this monograph useful not only for experts but also as a text for advanced graduate courses. Historical notes appear at the endof each chapter, and a list of Open Problems and Questions is provided to stimulate further research in this area. With over 400 references, Extensions of Rings and Modules will be o f interest to researchers in algebra and analysis andto advanced graduate students in mathematics
Note:Springer eBooks
Contents:Preliminaries and Basic Results
Injectivity and Some of Its Generalizations
Baer, Rickart, and Quasi
Baer Rings
Baer, Quasi
Baer Modules, and Their Applications
Triangular Matrix Representations and Triangular Matrix Extensions
Matrix, Polynomial, and Group Ring Extensions
Essential Overring Extensions
Beyond the Maximal Ring of Quotients
Ring and Module Hulls
Hulls of Ring Extensions
Applications to Rings of Quotients and C* Algebras
Open Problems and Questions
References
Index
ISBN:9780387927169
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Matrix theory , Functional analysis
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Call number:SPRINGER-2012-9783642308048:ONLINE Show nearby items on shelf
Title:An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists [electronic resource]
Author(s): Hajime Ishimori
Tatsuo Kobayashi
Hiroshi Ohki
Hiroshi Okada
Yusuke Shimizu
Morimitsu Tanimoto
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:9783642308048
Series:Lecture Notes in Physics
Series:e-books
Keywords: Elementary Particles, Quantum Field Theory , Mathematical Methods in Physics , Mathematical Physics , Group Theory and Generalizations
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Call number:SPRINGER-2012-9781461400288:ONLINE Show nearby items on shelf
Title:Partitions, q-Series, and Modular Forms [electronic resource]
Author(s): Krishnaswami Alladi
Frank Garvan
Date:2012
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book contains a unique collection of both research and survey papers written by an international group of some of the world's experts on partitions, q-series, and modular forms, as outgrowths of a conference held at theUniversity of Florida, Gai nesville in March 2008. The success of this conference has led to annual year-long programs in Algebra, Number Theory, and Combinatorics (ANTC) at the university. A common theme in the book is the study ofq-series, an area which in recent years has witnes sed dramatic advances having significant impact on a variety of fields within and outside of mathematics such as physics. Most major aspects of the modern theory of q-series and howthey relate to number theory, combinatorics, and special functions are rep resented in this volume. Topics include the theory of partitions via computer algebra, elementary asymptotic methods expositions on Ramanujan's mocktheta-functions emphasizing the classical aspects as well as the recent exciting connections with the theor y of harmonic Maass forms congruences for modular forms a study of theta-functions from elementary, function-theoretic andRiemann surface viewpoints and a systematic analysis of multiple basic hypergeometric functions associated with root systems of Lie a lgebras. The broad range of topics covered in this volume will be of interest to both researchersand graduate students who want to learn of recent developments in the theory of partitions, q-series and modular forms and their far reaching impact on divers e areas of mathematics
Note:Springer eBooks
Contents:Preface(K. Alladi and F. Garvan)
1. MacMahon's dream (G. E. Andrews andP. Paule)
2. Ramanujan's elementary method in partition congruences (B. Berndt, C. Gugg, and S. Kim)
3. Coefficients of harmonic Maass forms (K. Bringmann and K. Ono)
4. On the growth of restricted partition functions (E. R. Canfield and H. Wilf)
5. On applications of roots of unity to product identities (Z. Cao)
6. Lecture hall sequences, q
series, and asymmetric partition identities (S. Corteel, C. Savage and A. Sills)
7. Generalizations of Hutchinson's curve and the Thomae formula (H. Farkas)
ISBN:9781461400288
Series:e-books
Series:SpringerLink (Online service)
Series:Developments in Mathematics, 1389-2177 : v23
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions, special , Combinatorics , Number theory
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Call number:SPRINGER-2011-9780817647414:ONLINE Show nearby items on shelf
Title:Developments and Trends in Infinite-Dimensional Lie Theory [electronic resource]
Author(s): Karl-Hermann Neeb
Arturo Pianzola
Date:2011
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
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Note:This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts:infinite-dimensional Lie ( super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Part (A) is mainly concerned with the structure and representationtheory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and KacMoody superalgebras.The articles in Part (B) examine connections between infinite-dimension al Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, toJordan-theoretic geometries and new results on direct-limit groups. The analytic representation theor y of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods basedon heat kernels, multiplicity freeness, BanachLiePoisson spaces, and infinite-dimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Belti, W. Bertram, J. Faulkner, Ph. Gille, H. Glckner, K.-H.Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf
Note:Springer eBooks
Contents:Preface
Part A: Infinite
Dimensional Lie (Super
)Algebras
Isotopy for Extended Affine Lie Algebras and Lie Tori
Remarks on the Isotriviality of Multiloop Algebras
Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras A Survey
Tensor Representations of Classical Locally Finite Lie Algebras
Lie Algebras, Vertex Algebras, and Automorphic Forms
KacMoody Superalgebras and Integrability
Part B: Geometry of Infinite
Dimensional Lie (Transformation) Groups
Jordan Structures and Non
Associative Geometry
Direct Limits of Infinite
Dimensional L
ISBN:9780817647414
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v288
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Group theory , Topological Groups , Geometry
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Call number:SPRINGER-2010-9780817649326:ONLINE Show nearby items on shelf
Title:Topics in Operator Semigroups [electronic resource]
Author(s): Shmuel Kantorovitz
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The theory of operator semigroups was essentially discovered in the early 1930s. Since then, the theory has developed into a rich and exciting area of functional analysis and has been applied to various mathematical topics suchas Markov processes, th e abstract Cauchy problem, evolution equations, and mathematical physics. This self-contained monograph focuses primarily on the theoretical connection between the theory of operator semigroups and spectraltheory. Divided into three parts with a total of twelve distinct chapters, this book gives an in-depth account of the subject with numerous examples, detailed proofs, and a brief look at a few applications. Topics include: * TheHilleYosida and LumerPhillips characterizations of semigroup generators * Th e TrotterKato approximation theorem * Katos unified treatment of the exponential formula and the Trotter product formula * The HillePhillipsperturbation theorem, and Stones representation of unitary semigroups * Generalizations of spectral theorys connect ion to operator semigroups * A natural generalization of Stones spectral integral representation to a Banachspace setting With a collection of miscellaneous exercises at the end of the book and an introductory chapter examining the basic theory involved, this monograph is suitable for second-year graduate students interested in operatorsemigroups
Note:Springer eBooks
Contents:General Theory
Basic Theory
The Semi
Simplicity Space for Groups
Analyticity
The Semigroup as a Function of its Generator
Large Parameter
Boundary Values
Pre
Semigroups
Integral Representations
The Semi
Simplicity Space
The LaplaceStieltjes Space
Families of Unbounded Symmetric Operators
A Taste of Applications
Analytic Families of Evolution Systems
Similarity
ISBN:9780817649326
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v281
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Operator theory
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Call number:SPRINGER-2009-9783764399900:ONLINE Show nearby items on shelf
Title:Regularity and Substructures of Hom [electronic resource]
Author(s): Friedrich Kasch
Adolf Mader
Date:2009
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The book generalizes the well-known regularity of ring elements to regularity of homomorphisms in module categories, and further to regularity of morphisms in any category. Regular homomorphisms are characterized in terms ofdecompositions of domain a nd codomain, and numerous other results are presented. While the theory is well developed in module categories many questions remain about generalizations and extensions to other categories. The book onlyrequires the knowledge of a basic course in modern algebra. It is written clearly, with great detail, and is accessible to students and researchers alike
Note:Springer eBooks
ISBN:9783764399900
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2008-9789491216350:ONLINE Show nearby items on shelf
Title:Topological Groups and Related Structures [electronic resource]
Author(s): Alexander Arhangelskii
Mikhail Tkachenko
Date:2008
Publisher:Paris : Atlantis Press
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, theobjects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groupsand semigroups, paratopological groups, etc. S pecial emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of theoperation. The main scope of the book, however, is outside of the loca lly compact structures, thus distinguishing the monograph from a series of more traditional textbooks. The book is unique in that it presents very importantmaterial, dispersed in hundreds of research articles, not covered by any monograph in existence. Th e reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the wayto the frontier of the knowledge is quite short almost every section of the book contains several intriguing open proble ms whose solutions can contribute significantly to the area
Note:Springer eBooks
ISBN:9789491216350
Series:e-books
Series:SpringerLink (Online service)
Series:Atlantis Studies in Mathematics, 1875-7634 : v1
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Algebraic topology
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Call number:SPRINGER-2006-9783764375362:ONLINE Show nearby items on shelf
Title:The Monodromy Group [electronic resource]
Author(s): Henryk odek
Date:2006
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:In singularity theory and algebraic geometry the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures.In the theory of syste ms of linear differential equations one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliationsthere appear the Ecalle-Voronin-Martinet-Ram is moduli. On the other hand, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. All this is presented in this book,underlining the unifying role of the monodromy group. The material is add ressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. The book contains a lot of resultswhich are usually spread in many sources. Readers can quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galoistheory, and parts of algebraic geometry, without searching in vast literature
Note:Springer eBooks
Contents:Analytic Functions and Morse Theory
Normal Forms of Functions
Algebraic Topology of Manifolds
Topology and Monodromy of Functions
Integrals along Vanishing Cycles
Vector Fields and Abelian Integrals
Hodge Structures and Period Map
Linear Differential Systems
Holomorphic Foliations. Local Theory
Holomorphic Foliations. Global Aspects
The Galois Theory
Hypergeometric Functions
ISBN:9783764375362
Series:e-books
Series:SpringerLink (Online service)
Series:Monografie Matematyczne : v67
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Functions of complex variables , Differential Equations , Functions, special , Algebraic topology
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Call number:SPRINGER-2006-9783540307310:ONLINE Show nearby items on shelf
Title:Self-Dual Codes and Invariant Theory [electronic resource]
Author(s): Gabriele Nebe
Eric M Rains
Neil J.A Sloane
Date:2006
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. In the past 35 years there have beenhundreds of papers written a bout generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations. It isalso in part an encyclopedia that gives a very exte nsive list of the different types of self-dual codes and their properties, including tables of the best codes that are presently known. Besides self-dual codes, the book also discussestwo closely-related subjects, lattices and modular forms, and quantum e rror-correcting codes. This book, written by the leading experts in the subject, has no equivalent in the literature and will be of great interest tomathematicians, communication theorists, computer scientists and physicists
Note:Springer eBooks
Contents:Preface
1 The Type of a Self
Dual Code
2 Weight Enumerators and Important Types
3 Closed Codes
4 The Category Quad
5 The Main Theorems
6 Real and Complex Clifford Groups
7 Classical Self
Dual Codes
8 Further Examples of Self
Dual Codes
9 Lattices
10 Maximal Isotropic Codes and Lattices
11 Extremal and Optimal Codes
12 Enumeration of Self
Dual Codes
13 Quantum Codes
Bibliography
Index
ISBN:9783540307310
Series:e-books
Series:SpringerLink (Online service)
Series:Algorithms and Computation in Mathematics, 1431-1550 : v17
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Coding theory , Algebra , Group theory , Number theory , Quantum computing
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Call number:SPRINGER-2006-9781402050107:ONLINE Show nearby items on shelf
Title:Automorphic Forms and Lie Superalgebras [electronic resource]
Author(s): Urmie Ray
Date:2006
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:A principal ingredient in the proof of the Moonshine Theorem, connecting the Monster group to modular forms, is the infinite dimensional Lie algebra of physical states of a chiral string on an orbifold of a 26 dimensional torus,called the Monster Lie algebra. It is a Borcherds-Kac-Moody Lie algebra with Lorentzian root lattice and has an associated automorphic form having a product expansion describing its structure. Lie superalgebras are generalizations ofLie algebras, useful for depicting supersymm etry the symmetry relating fermions and bosons. Most known examples of Lie superalgebras with a related automorphic form such as the Fake Monster Lie algebra whose reflection group isgiven by the Leech lattice arise from (super)string theory and can be d erived from lattice vertex algebras. The No-Ghost Theorem from dual resonance theory and a conjecture of Berger-Li-Sarnak on the eigenvalues of the hyperbolicLaplacian provide strong evidence that they are of rank at most 26. The aim of this book is to gi ve the reader the tools to understand the ongoing classification and construction project of this class of Lie superalgebras and is idealfor a graduate course. The necessary background is given within chapters or in appendices
Note:Springer eBooks
Contents:Borcherds
Kac
Moody Lie Superalgebras
Singular Theta Transforms of Vector Valued Modular Forms
?
Graded Vertex Algebras
Lorentzian BKM Algebras
ISBN:9781402050107
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications : v5
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Number theory
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Call number:SPRINGER-2006-9780387316079:ONLINE Show nearby items on shelf
Title:Binomial Models in Finance [electronic resource]
Author(s): John Hoek
Robert J Elliott
Date:2006
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book deals with many topics in modern financial mathematics in a way that does not use advanced mathematical tools and shows how these models can be numerically implemented in a practical way. The book is aimed atundergraduate students, MBA stud ents, and executives who wish to understand and apply financial models in the spreadsheet computing environment. The basic building block is the one-step binomial model where a known price today can takeone of two possible values at the next time. In this simple situation, risk neutral pricing can be defined and the model can be applied to price forward contracts, exchange rate contracts, and interest rate derivatives. The simpleone-period framework can then be extended to multi-period models. The authors show how binomial tree models can be constructed for several applications to bring about valuations consistent with market prices. The book closes with anovel discussion of real options. John van der Hoek is Senior Lecturer in Applied Mathematics at the University of Adelaide. He has developed courses in finance for a number of years at various levels and is a regular plenary speakerat major conferences on Quantitative Finance. Robert J. Elliott is RBC Financial Group Professor of Finance at the Haskayne School of Business at the University of Calgary. He is the author of over 300 research papers and severalbooks, including Mathematics of Financial Markets, Second Edition (with P. Ekkehard Kopp), Stochastic Calculus and Applications, Hidden Markov Models (with Lahkdar Aggoun and John Moore) and Measure Theory and Filtering: Theory andApplications (with Lakhdar Aggoun). He is an Associate Editor of Mathematical Finance, Stochastics and Stochastics Reports, Stochastic Analysis and Applications, and the Can adian Applied Mathematics Quarterly
Note:Springer eBooks
Contents:Introduction
The binomial model for stock options
The binomial model for other contracts
Multiperiod binomial models
Hedging
Forward and futures contracts
American and exotic option pricing
Path dependent options
The Greeks
Dividends
Implied volatility trees
Implied binomial trees
Interest rate models
Real options
The binomial distribution
An application of linear programming
Volatility estimation
Existence of a solution
Some generalizations
Yield curves and splines
ISBN:9780387316079
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Finance
Series:Mathematics and Statistics (Springer-11649)
Keywords: Statistics , Finance , Economics Statistics , Economics, Mathematical
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Call number:SPRINGER-2004-9783764378011:ONLINE Show nearby items on shelf
Title:Rings, Modules, and the Total
Author(s): Friedrich Kasch
Date:2004
Size:1 online resource (138 p.)
Note:10.1007/b96769
Contents:Preface -- General Background -- I. Fundamental Notions and Properties -- II. Good Conditions for the Total -- III. The Total of Modules with LE-decompositions -- IV. The Total in Torsion-Free Abelian Groups -- Bibliography -- Index
ISBN:9783764378011
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Associative rings , Rings (Algebra) , Group theory , Mathematics , Algebra , Associative Rings and Algebras , Group Theory and Generalizations
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Call number:SPRINGER-2004-9783662062807:ONLINE Show nearby items on shelf
Title:Cohomology of Finite Groups
Author(s): Alejandro Adem
Date:2004
Edition:Second Edition
Size:1 online resource (324 p.)
Note:10.1007/978-3-662-06280-7
Contents:I. Group Extensions, Simple Algebras and Cohomology -- II. Classifying Spaces and Group Cohomology -- III. Invariants and Cohomology of Groups -- IV. Spectral Sequences and Detection Theorems -- V. G-Complexes and Equivariant
Cohomology -- VI. The Cohomology of the Symmetric Groups -- VII. Finite Groups of Lie Type -- VIII. Cohomology of Sporadic Simple Groups -- IX. The Plus Construction and Applications -- X. The Schur Subgroup of the Brauer Group --
References
ISBN:9783662062807
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics: 309
Keywords: Mathematics , Algebra , Group theory , K-theory , Algebraic topology , Mathematics , Algebra , Group Theory and Generalizations , Algebraic Topology , K-Theory
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Call number:SPRINGER-2004-9783540445098:ONLINE Show nearby items on shelf
Title:The Theory of Symmetry Actions in Quantum Mechanics with an Application to the Galilei Group
Author(s): Gianni Cassinelli
Date:2004
Size:1 online resource (111 p.)
Note:10.1007/b99455
Contents:A Synopsis of Quantum Mechanics -- The Automorphism Group of Quantum Mechanics -- The Symmetry Actions and Their Representations -- The Galilei Groups -- Galilei Invariant Elementary Particles -- Galilei Invariant Wave Equations
ISBN:9783540445098
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Physics: 654
Keywords: Physics , Group theory , Topological groups , Lie groups , Quantum physics , Physics , Mathematical Methods in Physics , Quantum Physics , Topological Groups, Lie Groups , Group Theory and Generalizations
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Call number:SPRINGER-2004-9783540409984:ONLINE Show nearby items on shelf
Title:Methods of Graded Rings
Author(s): Constantin Nastasescu
Date:2004
Size:1 online resource (306 p.)
Note:10.1007/b94904
Contents:The Category of Graded Rings -- The Category of Graded Modules -- Modules over Stronly Graded Rings -- Graded Clifford Theory -- Internal Homogenization -- External Homogenization -- Smash Products -- Localization of Graded Rings --
Application to Gradability -- Appendix A: Some Category Theory -- Appendix B: Dimensions in an Abelian Category -- Bibliography -- Index
ISBN:9783540409984
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1836
Keywords: Mathematics , Algebra , Associative rings , Rings (Algebra) , Category theory (Mathematics) , Homological algebra , Group theory , Physics , Mathematics , Algebra , Associative Rings and Algebras , Category Theory, Homological Algebra , Group Theory and Generalizations , Mathematical Methods in Physics
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Call number:SPRINGER-2004-9783034878876:ONLINE Show nearby items on shelf
Title:Dynamics of Foliations, Groups and Pseudogroups
Author(s): Paweł Walczak
Date:2004
Size:1 online resource (228 p.)
Note:10.1007/978-3-0348-7887-6
Contents:1 Dynamical systems -- 1.1 Pseudogroups -- 1.2 First examples -- 1.3 Foliations, laminations and holonomy -- 1.4 Markov pseudogroups -- 1.5 Hyperbolic spaces and groups -- 2 Growth -- 2.1 Growth types -- 2.2 Growth in groups -- 2.3
Orbit growth for pseudogroups -- 2.4 Expansion growth -- 3 Entropy -- 3.1 Entropy of classical systems -- 3.2 Entropy of pseudogroups -- 3.3 Geometric entropy of foliations -- 3.4 Relating various entropies -- 3.5 Examples and
constructions -- 3.6 Entropy and resiliency -- 4 Invariant measures -- 4.1 Basic definitions and facts -- 4.2 Transverse invariant measures and homology -- 4.3 Measures and orbit growth -- 4.4 Transverse invariant measures in
codimension 1 -- 4.5 Vanishing entropy and invariant measures -- 4.6 Entropy, geodesic flow and invariant measures -- 4.7 Harmonic measures -- 4.8 Patterson—Sullivan measures -- 5 Hausdorff dimension -- 5.1 Definitions and basic facts
-- 5.2 Julia sets -- 5.3 Dimension in foliated manifolds -- 5.4 Dimension of a hyperbolic boundary -- 5.5 Dimension of a limit set -- 6 Varia -- 6.1 Complexity growth -- 6.2 Expansive systems -- 6.3 Pseudo-orbits and pseudoleaves --
6.4 Generic leaves
ISBN:9783034878876
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Monografie Matematyczne : 64
Keywords: Mathematics , Group theory , Topological groups , Lie groups , Dynamics , Ergodic theory , Differential geometry , Mathematics , Group Theory and Generalizations , Topological Groups, Lie Groups , Dynamical Systems and Ergodic Theory , Differential Geometry
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Call number:SPRINGER-2004-9781475740943:ONLINE Show nearby items on shelf
Title:Lie Groups
Author(s): Daniel Bump
Date:2004
Size:1 online resource (454 p.)
Note:10.1007/978-1-4757-4094-3
Contents:1 Haar Measure -- 2 Schur Orthogonality -- 3 Compact Operators -- 4 The Peter-Weyl Theorem -- 5 Lie Subgroups of GL(n, ?) -- 6 Vector Fields -- 7 Left-Invariant Vector Fields -- 8 The Exponential Map -- 9 Tensors and Universal
Properties -- 10 The Universal Enveloping Algebra -- 11 Extension of Scalars -- 12 Representations of sl(2, ?) -- 13 The Universal Cover -- 14 The Local Frobenius Theorem -- 15 Tori -- 16 Geodesics and Maximal Tori -- 17 Topological
Proof of Cartan’s Theorem -- 18 The Weyl Integration Formula -- 19 The Root System -- 20 Examples of Root Systems -- 21 Abstract Weyl Groups -- 22 The Fundamental Group -- 23 Semisimple Compact Groups -- 24 Highest-Weight Vectors -- 25
The Weyl Character Formula -- 26 Spin -- 27 Complexification -- 28 Coxeter Groups -- 29 The Iwasawa Decomposition -- 30 The Bruhat Decomposition -- 31 Symmetric Spaces -- 32 Relative Root Systems -- 33 Embeddings of Lie Groups -- 34
Mackey Theory -- 35 Characters of GL(n, ?) -- 36 Duality between Sk and GL(n, ?) -- 37 The Jacobi-Trudi Identity -- 38 Schur Polynomials and GL(n, ?) -- 39 Schur Polynomials and Sk -- 40 Random Matrix Theory -- 41 Minors of Toeplitz
Matrices -- 42 Branching Formulae and Tableaux -- 43 The Cauchy Identity -- 44 Unitary Branching Rules -- 45 The Involution Model for Sk -- 46 Some Symmetric Algebras -- 47 Gelfand Pairs -- 48 Hecke Algebras -- 49 The Philosophy of
Cusp Forms -- 50 Cohomology of Grassmannians -- References
ISBN:9781475740943
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Graduate Texts in Mathematics: 225
Keywords: Mathematics , Group theory , Topological groups , Lie groups , Mathematics , Topological Groups, Lie Groups , Group Theory and Generalizations
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Call number:SPRINGER-2004-9781475738117:ONLINE Show nearby items on shelf
Title:Momentum Maps and Hamiltonian Reduction
Author(s): Juan-Pablo Ortega
Date:2004
Size:1 online resource (501 p.)
Note:10.1007/978-1-4757-3811-7
Contents:1 Manifolds and Smooth Structures -- 2 Lie Group Actions -- 3 Pseudogroups and Groupoids -- 4 The Standard Momentum Map -- 5 Generalizations of the Momentum Map -- 6 Regular Symplectic Reduction Theory -- 7 The Symplectic Slice
Theorem -- 8 Singular Reduction and the Stratification Theorem -- 9 Optimal Reduction -- 10 Poisson Reduction -- 11 Dual Pairs
ISBN:9781475738117
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics : 222
Keywords: Mathematics , Topological groups , Lie groups , Differential equations , Applied mathematics , Engineering mathematics , Physics , Mathematics , Topological Groups, Lie Groups , Ordinary Differential Equations , Applications of Mathematics , Mathematical Methods in Physics
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Call number:SPRINGER-2004-9781468493832:ONLINE Show nearby items on shelf
Title:Primer for Point and Space Groups
Author(s): Richard L Liboff
Date:2004
Size:1 online resource (220 p.)
Note:10.1007/978-1-4684-9383-2
Contents:1 Groups and Subgroups -- 1.1 Definitions and Basics -- 1.2 Group Table -- 1.3 Rearrangement Theorem -- 1.4 Building Groups. Subgroups -- Summary of Topics for Chapter 1 -- Problems -- 2 Classes and Platonic Solids -- 2.1 Conjugate
Elements -- 2.2 Classes -- 2.3 Direct Product -- 2.4 Cnv and Dn Groups -- 2.5 Platonic Solids. T, O and I Groups -- Summary of Topics for Chapter 2 -- Problems -- 3 Matrices, Irreps and the Great Orthogonality Theorem -- 3.1 Matrix
Representations of Operators -- 3.2 Irreducible Representations -- 3.3 Great Orthogonality Theorem (GOT) -- 3.4 Six Important Rules -- 3.5 Character Tables. Bases -- 3.6 Representations of Cyclic Groups -- Summary of Topics for Chapter
3 -- Problems -- 4 Quantum Mechanics, the Full Rotation Group, and Young Diagrams -- 4.1 Application to Quantum Mechanics -- 4.2 Full Rotation Group O(3) -- 4.3 SU(2) -- 4.4 Irreps of O(3)+ and Coupled Angular Momentum States -- 4.5
Symmetric Group Cayley’s Theorem -- 4.6 Young Diagrams -- 4.7 Degenerate Perturbation Theory -- Summary of Topics for Chapter 4 -- Problems -- 5 Space Groups, Brillouin Zone and the Group of k -- 5.1 Cosets and Invariant Subgroups. The
Factor Group -- 5.2 Primitive Vectors. Braviais Lattice. Reciprocal Lattice Space -- 5.3 Crystallographic Point Groups and Reciprocal Lattice Space -- 5.4 Bloch Waves and Space Groups -- 5.5 Application to Semiconductor Materials --
5.6 Time Reversal, Space Inversion and Double Space Groups -- Summary of Topics for Chapter 5 -- Problems -- 6 Atoms in Crystals and Correlation Diagrams -- 6.1 Central-Field Approximation -- 6.2 Atoms in Crystal Fields -- 6.3
Correlation Diagrams -- 6.4 Electric and Magnetic Material Properties -- 6.5 Tensors in Group Theory -- Summary of Topics for Chapter 6 -- Problems -- 7 Elements of Abstract Algebra and the Galois Group -- 7.1 Integral Domains, Rings
and Fields -- 7.2 Numbers -- 7.3 Irreducible Polynomials -- 7.4 The Galois Group -- Symbols for Chapter 7 -- Summary of Topics for Chapter 7 -- Problems -- Appendix A: Character Tables for the Point Groups -- Bibliography of Works in
Group Theory and Allied Topics
ISBN:9781468493832
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Physical chemistry , Group theory , Condensed matter , Electrical engineering , Physics , Physics, general , Physical Chemistry , Group Theory and Generalizations , Condensed Matter Physics , Electrical Engineering
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Call number:SPRINGER-2004-9781461302490:ONLINE Show nearby items on shelf
Title:Galois Theory and Modular Forms
Author(s):
Date:2004
Size:1 online resource (394 p.)
Note:10.1007/978-1-4613-0249-0
Contents:I. Arithmetic geometry -- The arithmetic of Weierstrass points on modular curves X0(p) -- Semistable abelian varieties with small division fields -- Q-curves with rational j-invariants and jacobian surfaces of GL2-type -- Points
defined over cyclic quartic extensions on an elliptic curve and generalized Kummer surfaces -- The absolute anabelian geometry of hyperbolic curves -- II. Galois groups and Galois extensions -- Regular Galois realizations of PSL2(p2)
over ?(T) -- Middle convolution and Galois realizations -- On the essential dimension of p-groups -- Explicit constructions of generic polynomials for some elementary groups -- On dihedral extensions and Frobenius extensions -- On the
non-existence of certain Galois extensions -- Frobenius modules and Galois groups -- III. Algebraic number theory -- On quadratic number fields each having an unramified extension which properly contains the Hilbert class field of its
genus field -- Distribution of units of an algebraic number field -- On capitulation problem for 3-manifolds -- On the Iwasawa ?-invariant of the cyclotomic ?p-extension of certain quartic fields -- IV. Modular forms and arithmetic
functions -- Quasimodular solutions of a differential equation of hypergeometric type -- Special values of the standard zeta functions -- p-adic properties of values of the modular j-function -- Thompson series and Ramanujan’s
identities -- Generalized Rademacher functions and some congruence properties
ISBN:9781461302490
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Developments in Mathematics: 11
Keywords: Mathematics , Algebraic geometry , Algebra , Field theory (Physics) , Group theory , Mathematics , Field Theory and Polynomials , Algebraic Geometry , Group Theory and Generalizations
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Call number:SPRINGER-2004-9781402045226:ONLINE Show nearby items on shelf
Title:Concise Encyclopedia of Supersymmetry And noncommutative structures in mathematics and physics
Author(s): Steven Duplij
Date:2004
Size:1 online resource (eReference p.)
Note:10.1007/1-4020-4522-0
ISBN:9781402045226
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Group theory , Nonassociative rings , Rings (Algebra) , Physics , Theoretical, Mathematical and Computational Physics , Non-associative Rings and Algebras , Group Theory and Generalizations
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Call number:SPRINGER-2004-9781402025471:ONLINE Show nearby items on shelf
Title:Handbook of Number Theory II
Author(s): J Sándor
Date:2004
Size:1 online resource (eReference p.)
Note:10.1007/1-4020-2547-5
Contents:From the contents: Preface -- Basic Symbols -- Basic Notations -- Perfect Numbers: Old and New Issues: Perspectives -- Generalizations and Extensions of the Möbius Function -- The many Facets of Euler’s Totient -- Special Arithmetic
Function connected with the Divisors, or with the Digits of a Number -- Sterling, Bell, Bernoulli, Euler and Eulerian Numbers -- Reference -- Index
ISBN:9781402025471
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Group theory , Numerical analysis , Number theory , Probabilities , Combinatorics , Mathematics , Number Theory , Combinatorics , Probability Theory and Stochastic Processes , Numerical Analysis , Group Theory and Generalizations
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Call number:SPRINGER-2004-9781402021879:ONLINE Show nearby items on shelf
Title:Abel’s Theorem in Problems and Solutions Based on the lectures of Professor V.I. Arnold
Author(s): V.B Alekseev
Date:2004
Size:1 online resource (270 p.)
Note:10.1007/1-4020-2187-9
Contents:From the contents: Preface for the English edition V.I. Arnold -- Preface -- Introduction -- 1: Groups -- 2: The complex numbers -- 3: Hints, Solutions and Answers -- Appendix. Solvability of equations by explicit formulae A.
Khovanskii -- Bibliography -- Appendix V.I. Arnold -- Index
ISBN:9781402021879
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Field theory (Physics) , Group theory , Topological groups , Lie groups , Functions of complex variables , Mathematics , Group Theory and Generalizations , Functions of a Complex Variable , Field Theory and Polynomials , Topological Groups, Lie Groups
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Call number:SPRINGER-2004-9780817681920:ONLINE Show nearby items on shelf
Title:Lie Theory Lie Algebras and Representations
Author(s): Jens Carsten Jantzen
Date:2004
Size:1 online resource (331 p.)
Note:10.1007/978-0-8176-8192-0
Contents:Preface -- Nilpotent Orbits in Representation Theory -- 1 Nilpotent Orbits for Classical Groups -- 2 Some General Results -- 3 Centralizers in the Classical Cases -- 4 Bala-Carter Theory -- 5 Centralizers -- 6 The Nilpotent Cone I --
7 The Nilpotent Cone II -- 8 Functions on Orbits and Orbit Closures -- 9 Associated Varieties -- 10 Springer’s Fibers and Steinberg’s Triples -- 11 Paving Springer’s Fibers -- 12 ?-adic and Perverse Stuff -- 13 Springer’s
Representations -- References -- Infinite-Dimensional Groups and Their Representations -- I The Finite-Dimensional Case -- II Split Lie Algebras -- III Unitary Highest Weight Modules -- IV Banach-Lie Groups -- V Holomorphic
Representations of Classical Banach-Lie Groups -- VI Geometry of Coadjoint Orbits of Banach-Lie Groups -- VII Coadjoint Orbits and Complex Line Bundles for U2(H) -- Appendix: The Topology of Classical Banach-Lie Groups -- References
ISBN:9780817681920
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics : 228
Keywords: Mathematics , Algebra , Group theory , Topological groups , Lie groups , Harmonic analysis , Geometry , Number theory , Mathematics , Topological Groups, Lie Groups , Algebra , Group Theory and Generalizations , Abstract Harmonic Analysis , Geometry , Number Theory
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Call number:SPRINGER-2004-9780387217680:ONLINE Show nearby items on shelf
Title:The Theory of Finite Groups An Introduction
Author(s): Hans Kurzweil
Date:2004
Size:1 online resource (388 p.)
Note:10.1007/b97433
Contents:Basic Concepts -- Abelian Groups -- Action and Conjugation -- Permutation Groups -- p-Groups and Nilpotent Groups -- Normal and Subnormal Structure -- Transfer and p-Factor Groups -- Groups Acting on Groups -- Quadratic Action -- The
Embedding of p-Local Subgroups -- Signalizer Functors -- N-Groups
ISBN:9780387217680
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Group theory , Mathematics , Group Theory and Generalizations
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Call number:SPRINGER-2003-9789401703451:ONLINE Show nearby items on shelf
Title:Endomorphism Rings of Abelian Groups
Author(s): Piotr A Krylov
Date:2003
Size:1 online resource (443 p.)
Note:10.1007/978-94-017-0345-1
Contents:I. General Results on Endomorphism Rings -- II. Groups as Modules over Their Endomorphism Rings -- III. Ring Properties of Endomorphism Rings -- IV. The Jacobson Radical of the Endomorphism Ring -- V. Isomorphism and Realization
Theorems -- VI. Hereditary Endomorphism Rings -- VII. Fully Transitive Groups -- References
ISBN:9789401703451
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Algebras and Applications: 2
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Group theory , Mathematics , Associative Rings and Algebras , Group Theory and Generalizations , Commutative Rings and Algebras
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Call number:SPRINGER-2003-9789401703390:ONLINE Show nearby items on shelf
Title:Exercises in Abelian Group Theory
Author(s): Grigore Călugăreanu
Date:2003
Size:1 online resource (351 p.)
Note:10.1007/978-94-017-0339-0
Contents:1 Basic notions -- 2 Divisible groups -- 3 Pure subgroups -- 4 Topological groups -- 5 Algebraically compact groups -- 6 Homological methods -- 7 p-groups -- 8 Torsion-free groups -- 9 Mixed groups -- 10 Subgroup lattices of groups --
1 Basic notions -- 2 Divisible groups -- 3 Pure subgroups -- 4 Topological groups -- 5 Algebraically comact groups -- 6 Homological methods -- 7 p-groups -- 8 Torsion-free groups -- 9 Mixed groups -- 10 Subgroup lattices of groups
ISBN:9789401703390
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Texts in the Mathematical Sciences: 25
Keywords: Mathematics , Category theory (Mathematics) , Homological algebra , Group theory , Algebra , Ordered algebraic structures , Topological groups , Lie groups , Mathematics , Group Theory and Generalizations , Topological Groups, Lie Groups , Category Theory, Homological Algebra , Order, Lattices, Ordered Algebraic Structures
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Call number:SPRINGER-2003-9789401703376:ONLINE Show nearby items on shelf
Title:Proceedings of the Third International Algebra Conference June 16–July 1, 2002 Chang Jung Christian University, Tainan, Taiwan
Author(s): Yuen Fong
Date:2003
Size:1 online resource (268 p.)
Note:10.1007/978-94-017-0337-6
ISBN:9789401703376
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Algebra , Field theory (Physics) , Group theory , Nonassociative rings , Mathematics , Field Theory and Polynomials , Commutative Rings and Algebras , Associative Rings and Algebras , Non-associative Rings and Algebras , Group Theory and Generalizations
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Call number:SPRINGER-2003-9789401702317:ONLINE Show nearby items on shelf
Title:Topological and Algebraic Structures in Fuzzy Sets A Handbook of Recent Developments in the Mathematics of Fuzzy Sets
Author(s):
Date:2003
Size:1 online resource (470 p.)
Note:10.1007/978-94-017-0231-7
Contents:1: Uniform Completion In Pointfree Topology -- 2: Monadic Convergence Structures -- 3: A Unified Approach To The Concept Of Fuzzy L-Uniform Space -- 4: Many Valued Topologies And Borel Probability Measures -- 5: Fuzzy Reals:
Topological Results Surveyed, Brouwer Fixed Point Theorem, Open Questions -- 6: Lattice-Valued Frames, Functor Categories, And Classes of Sober Spaces -- Appendix to Chapter 6: Weakening The Requirement That L Be A Complete Chain -- 7:
Axiomatic Foundations For Uniform Operator Quasi-Uniformities -- 8: Fully Fuzzy Topology -- 9: Fuzzy Logics Arising From Strict De Morgan Systems -- 10: Structure Of Girard Monoids on [0,1] -- 11: On The Geometry Of Choice -- 12: On
Some Fuzzy Categories Related To Category L-TOP Of L-Topological Spaces -- 13: Fuzzy Compactness Via Categorical Closure Operators -- 14: Discrete Triangular Norms -- 15: Powerset Operators Based Approach To Fuzzy Topologies On Fuzzy
Sets -- 16: Lifting Of Sobriety Concepts With Particular Reference To (L, M)-Topological Spaces -- 17: Examples For Different Sobrieties In Fixed-Basis Topology -- 18: Additive Generators Of Non-Continuous Triangular Norms -- 19:
Groups, T-Norms, And Families Of De Morgan Systems
ISBN:9789401702317
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Trends in Logic, Studia Logica Library: 20
Keywords: Mathematics , Logic , Group theory , Algebra , Ordered algebraic structures , Geometry , Mathematical logic , Mathematics , Mathematical Logic and Foundations , Geometry , Order, Lattices, Ordered Algebraic Structures , Group Theory and Generalizations , Logic
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Call number:SPRINGER-2003-9783642557293:ONLINE Show nearby items on shelf
Title:Mathematical Concepts of Quantum Mechanics
Author(s): Stephen J Gustafson
Date:2003
Size:1 online resource (253 p.)
Note:10.1007/978-3-642-55729-3
Contents:1 Physical Background -- 1.1 The Double-Slit Experiment -- 1.2 Wave Functions -- 1.3 State Space -- 1.4 The Schrödinger Equation -- 1.5 Mathematical Supplement: Operators on Hilbert Spaces -- 2 Dynamics -- 2.1 Conservation of
Probability -- 2.2 Existence of Dynamics -- 2.3 The Free Propagator -- 2.4 Mathematical Supplement: Operator Adjoints -- 2.5 Mathematical Supplement: the Fourier Transform -- 3 Observables -- 3.1 Mean Values and the Momentum Operator
-- 3.2 Observables -- 3.3 The Heisenberg Representation -- 3.4 Quantization -- 3.5 Pseudodifferential Operators -- 4 The Uncertainty Principle -- 4.1 The Heisenberg Uncertainty Principle -- 4.2 A Refined Uncertainty Principle -- 4.3
Application: Stability of Hydrogen -- 5 Spectral Theory -- 5.1 The Spectrum of an Operator -- 5.2 Functions of Operators and the Spectral Mapping Theorem -- 5.3 Applications to Schrödinger Operators -- 5.4 Spectrum and Evolution -- 5.5
Variational Characterization of Eigenvalues -- 5.6 Number of Bound States -- 5.7 Mathematical Supplement: Integral Operators -- 6 Scattering States -- 6.1 Short-range Interactions: µ > 1 -- 6.2 Long-range Interactions: µ ? 1 -- 6.3
Existence of Wave Operators -- 7 Special Cases -- 7.1 The Infinite Well -- 7.2 The Torus -- 7.3 A Potential Step -- 7.4 The Square Well -- 7.5 The Harmonic Oscillator -- 7.6 A Particle on a Sphere -- 7.7 The Hydrogen Atom -- 7.8 A
Particle in an External EM Field -- 8 Many-particle Systems -- 8.1 Quantization of a Many-particle System -- 8.2 Separation of the Centre-of-mass Motion -- 8.3 Break-ups -- 8.4 The HVZ Theorem -- 8.5 Intra- vs. Inter-cluster Motion --
8.6 Existence of Bound States for Atoms and Molecules -- 8.7 Scattering States -- 8.8 Mathematical Supplement: Tensor Products -- 9 Density Matrices -- 9.1 Introduction -- 9.2 States and Dynamics -- 9.3 Open Systems -- 9.4 The
Thermodynamic Limit -- 9.5 Equilibrium States -- 9.6 The T ? 0 Limit -- 9.7 Example: a System of Harmonic Oscillators -- 9.8 A Particle Coupled to a Reservoir -- 9.9 Quantum Systems -- 9.10 Problems -- 9.11 Hilbert Space Approach --
9.12 Appendix: the Ideal Bose Gas -- 9.13 Appendix: Bose-Einst ein Condensation -- 9.14 Mathematical Supplement: the Trace, and Trace Class Operators -- 10 The Feynman Path Integral -- 10.1 The Feynman Path Integral -- 10.2
Generalizations of the Path Integral -- 10.3 Mathematical Supplement: the Trotter Product Formula -- 11 Quasi-classical Analysis -- 11.1 Quasi-classical Asymptotics of the Propagator -- 11.2 Quasi-classical Asymptotics of Green’s
Function -- 11.3 Bohr-Sommerfeld Semi-classical Quantization -- 11.4 Quasi-classical Asymptotics for the Ground State Energy -- 11.5 Mathematical Supplement: Operator Determinants -- 12 Mathematical Supplement: the Calculus of
Variations -- 12.1 Functionals -- 12.2 The First Variation and Critical Points -- 12.3 Constrain ed Variational Problems -- 12.4 The Second Variation -- 12.5 Conjugate Points and Jacobi Fields -- 12.6 The Action of the Critical Path --
12.7 Appendix: Connection to Geodesics -- 13 Resonances -- 13.1 Tunneling and Resonances -- 13.2 The Free Resonance Energy -- 13.3 Instantons -- 13.4 Positive Temperatures -- 13.5 Pre-exponential Factor for the Bounce -- 13.6
Contribution of the Zero-mode -- 13.7 Bohr-Sommerfeld Quantization for Resonances -- 14 Introduction to Quantum Field Theory -- 14.1 The Place of QFT -- 14.2 Klein-Gordon Theory as a Hamiltonian System -- 14.3 Maxwell’s Equations as a
Hamiltonian System -- 14.4 Quantization of the Klein-Gordon and Maxwell Equations -- 14.5 Fock Space -- 14.6 Generalized Free Theory -- 14.7 Interactions -- 14.8 Quadratic Approximation -- 15 Quantum Electrodynamics of Non-relativistic
Particles: the Theory of Radiation -- 15.1 The Hamiltonian -- 15.2 Perturbation Set-up -- 15.3 Results -- 15.4 Mathematical Supplements -- 16 Supplement: Renormalization Group -- 16.1 The Decimation Map -- 16.2 Relative Bounds -- 16.3
Elimination of Particle and High Photon Energy Degrees of Freedom -- 16.4 Generalized Normal Form of Operators on Fock Space -- 16.5 The Hamiltonian H0(?, z) -- 16.6 A Banach Space of Operators -- 16.7 Rescaling -- 16.8 The
Renormalization Map -- 16.9 Linearized Flow -- 16.10 Central-stable Manifold for RG and Spectra of Hamiltonians -- 16.11 Appendix -- 17 Comments on Missing Topics, Literature, and Further Reading -- References
ISBN:9783642557293
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functional analysis , Physics , Quantum physics , Mathematics , Functional Analysis , Theoretical, Mathematical and Computational Physics , Quantum Physics
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Call number:SPRINGER-2003-9783540458050:ONLINE Show nearby items on shelf
Title:Coverings of Discrete Quasiperiodic Sets Theory and Applications to Quasicrystals
Author(s):
Date:2003
Size:1 online resource (273 p.)
Note:10.1007/3-540-45805-0
Contents:Covering of Discrete Quasiperiodic Sets: Concepts and Theory -- Covering Clusters in Icosahedral Quasicrystals -- Generation of Quasiperiodic Order by Maximal Cluster Covering -- Voronoi and Delone Clusters in Dual Quasiperiodic
Tilings -- The Efficiency of Delone Coverings of the Canonical Tilings ? *(a4) and ? *(d6) -- Lines and Planes in 2- and 3-Dimensional Quasicrystals -- Thermally-Induced Tile Rearrangements in Decagonal Quasicrystals — Superlattice
Ordering and Phason Fluctuation -- Tilings and Coverings of Quasicrystal Surfaces
ISBN:9783540458050
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Tracts in Modern Physics: 180
Keywords: Physics , Group theory , Crystallography , Phase transitions (Statistical physics) , Physics , Phase Transitions and Multiphase Systems , Crystallography , Group Theory and Generalizations
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Call number:SPRINGER-2003-9783540448907:ONLINE Show nearby items on shelf
Title:Asymptotic Combinatorics with Applications to Mathematical Physics A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia July 9–20, 2001
Author(s):
Date:2003
Size:1 online resource (250 p.)
Note:10.1007/3-540-44890-X
Contents:Random matrices, orthogonal polynomials and Riemann — Hilbert problem -- Asymptotic representation theory and Riemann — Hilbert problem -- Four Lectures on Random Matrix Theory -- Free Probability Theory and Random Matrices --
Algebraic geometry,symmetric functions and harmonic analysis -- A Noncommutative Version of Kerov’s Gaussian Limit for the Plancherel Measure of the Symmetric Group -- Random trees and moduli of curves -- An introduction to harmonic
analysis on the infinite symmetric group -- Two lectures on the asymptotic representation theory and statistics of Young diagrams -- III Combinatorics and representation theory -- Characters of symmetric groups and free cumulants --
Algebraic length and Poincaré series on reflection groups with applications to representations theory -- Mixed hook-length formula for degenerate a fine Hecke algebras
ISBN:9783540448907
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1815
Keywords: Mathematics , Group theory , Functional analysis , Partial differential equations , Applied mathematics , Engineering mathematics , Combinatorics , Physics , Mathematics , Applications of Mathematics , Physics, general , Combinatorics , Group Theory and Generalizations , Functional Analysis , Partial Differential Equations
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Call number:SPRINGER-2003-9783540396802:ONLINE Show nearby items on shelf
Title:Gröbner Bases and the Computation of Group Cohomology
Author(s):
Date:2003
Size:1 online resource (144 p.)
Note:10.1007/b93836
Contents:Introduction -- Part I Constructing minimal resolutions: Bases for finite-dimensional algebras and modules The Buchberger Algorithm for modules Constructing minimal resolutions -- Part II Cohomology ring structure: Gröbner bases for
graded commutative algebras The visible ring structure The completeness of the presentation -- Part III Experimental results: Experimental results -- A. Sample cohomology calculations -- Epilogue -- References -- Index
ISBN:9783540396802
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1828
Keywords: Mathematics , Associative rings , Rings (Algebra) , Group theory , Mathematics , Group Theory and Generalizations , Associative Rings and Algebras
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Call number:SPRINGER-2003-9783034889650:ONLINE Show nearby items on shelf
Title:Subgroup Growth
Author(s): Alexander Lubotzky
Date:2003
Size:1 online resource (454 p.)
Note:10.1007/978-3-0348-8965-0
Contents:0 Introduction and Overview -- 0.1 Preliminary comments and definitions -- 0.2 Overview of the chapters -- 0.3 On CFSG -- 0.4 The windows -- 0.5 The ‘notes’ -- 1 Basic Techniques of Subgroup Counting -- 1.1 Permutation representations
-- 1.2 Quotients and subgroups -- 1.3 Group extensions -- 1.4 Nilpotent and soluble groups -- 1.5 Abelian groups I -- 1.6 Finite p-groups -- 1.7 Sylow’s theorem -- 1.8 Rest riet ing to soluble subgroups -- 1.9 Applications of the
‘minimal index’ -- 1.10 Abelian groups II -- 1.11 Growth types -- Notes -- 2 Free Groups -- 2.1 The subgroup growth of free groups -- 2.2 Subnormal subgroups -- 2.3 Counting d-generator finite groups -- Notes -- 3 Groups with
Exponential Subgroup Growth -- 3.1 Upper bounds -- 3.2 Lower bounds -- 3.3 Free pro-p groups -- 3.4 Normal subgroups in free pro-p groups -- 3.5 Relations in p-groups and Lie algebras -- Notes -- 4 Pro-p Groups -- 4.1 Pro-p groups with
polynomial subgroup growth -- 4.2 Pro-p groups with slow subgroup growth -- 4.3 The groups $$SL_r^1({\mathbb{F}_p}[[t]])$$ -- 4.4 A-perfect groups -- 4.5 The Nottingham group -- 4.6 Finitely presented pro-p groups -- Notes -- 5
Finitely Generated Groups with Polynomial Subgroup Growth -- 5.1 Preliminary observations -- 5.2 Linear groups with PSG -- 5.3 Upper chief factors -- 5.4 Groups of prosoluble type -- 5.5 Groups of finite upper rank -- 5.6 The degree of
polynomial subgroup growth -- Notes -- 6 Congruence Subgroups -- 6.1 The characteristic 0 case -- 6.2 The positive characteristic case -- 6.3 Perfect Lie algebras -- 6.4 Normal congruence subgroups -- Notes -- 7 The Generalized
Congruence Subgroup Problem -- 7.1 The congruence subgroup problem -- 7.2 Subgroup growth of lattices -- 7.3 Counting hyperbolic manifolds -- Notes -- 8 Linear Groups -- 8.1 Subgroup growth, characteristic 0 -- 8.2 Residually nilpotent
groups -- 8.3 Subgroup growth, characteristic p -- 8.4 Normal subgroup growth -- Notes -- 9 Soluble Groups -- 9.1 Metabelian groups -- 9.2 Residually nilpotent groups -- 9.3 Some finitely presented metabelian groups -- 9.4 Normal
subgroup growth in metabelian groups -- Notes -- 10 Profinite Groups with Polynomial Subgroup Growth -- 10.1 Upper rank -- 10.2 Profinite groups with wPSG: structure -- 10.3 Quasi-semisimple groups -- 10.4 Profinite groups with wPSG:
characterization -- 10.5 Weak PSG = PSG -- Notes -- 11 Probabilistic Methods -- 11.1 The probability measure -- 11.2 Generation probabilities -- 11.3 Maximal subgroups -- 11.4 Further applications -- 11.5 Pro-p groups -- Notes -- 12
Other Growth Conditions -- 12.1 Rank and bounded generation -- 12.2 Adelic groups -- 12.3 The structure of finite linear groups -- 12.4 Composition factors -- 12.5 BG, PIG and subgroup growth -- 12.6 Residually nilpotent groups -- 12.7
Arithmetic groups and the CSP -- 12.8 Examples -- Notes -- 13 The Growth Spectrum -- 13.1 Products of alternating groups -- 13.2 Some finitely generated permutation groups -- 13.3 Some profinite groups with restricted composition
factors -- 13.4 Automorphisms of rooted trees -- Notes -- 14 Explicit Formulas and Asymptotics -- 14.1 Free groups and the modular group -- 14.2 Free products of finite groups -- 14.3 Modular subgroup arithmetic -- 14.4 Surface groups
-- Notes -- 15 Zeta Functions I: Nilpotent Groups -- 15.1 Local zeta functions as p-adic integrals -- 15.2 Alternative methods -- 15.3 The zeta function of a nilpotent group -- Notes -- 16 Zeta Functions II: p-adic Analytic Groups --
16.1 Integration on pro-p groups -- 16.2 Counting subgroups in a p-adic analytic group -- 16.3 Counting orbits -- 16.4 Counting p-groups -- Notes -- Windows -- 1 Finite Group Theory -- 2 Finite Simple Groups -- 3 Permutation Groups --
4 Profinite Groups -- 5 Pro-p Groups -- 6 Soluble Groups -- 7 Linear Groups -- 8 Linearity Conditions for Infinite Groups -- 9 Strong Approximation for Linear Groups -- 10 Primes -- 11 Probability -- 12 p-adic Integrals and Logic --
Open Problems
ISBN:9783034889650
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics : 212
Keywords: Mathematics , Science , Algebra , Group theory , Number theory , Mathematics , Algebra , Science, general , Group Theory and Generalizations , Number Theory
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Call number:SPRINGER-2003-9781475737141:ONLINE Show nearby items on shelf
Title:Applications of Hyperstructure Theory
Author(s): Piergiulio Corsini
Date:2003
Size:1 online resource (322 p.)
Note:10.1007/978-1-4757-3714-1
Contents:Basic notions and results on Hyperstructure Theory -- 1 Some topics of Geometry -- 2 Graphs and Hypergraphs -- 3 Binary Relations -- 4 Lattices -- 5 Fuzzy sets and rough sets -- 6 Automata -- 7 Cryptography -- 8 Codes -- 9 Median
algebras, Relation algebras, C-algebras -- 10 Artificial Intelligence -- 11 Probabilities
ISBN:9781475737141
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Advances in Mathematics : 5
Keywords: Mathematics , Computer science , Group theory , Algebra , Ordered algebraic structures , Mathematical logic , Combinatorics , Mathematics , Group Theory and Generalizations , Combinatorics , Mathematical Logic and Foundations , Discrete Mathematics in Computer Science , Order, Lattices, Ordered Algebraic Structures
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Call number:SPRINGER-2003-9781461200451:ONLINE Show nearby items on shelf
Title:Studies in Memory of Issai Schur
Author(s):
Date:2003
Size:1 online resource (369 p.)
Note:10.1007/978-1-4612-0045-1
Contents:Twisted Verma Modules -- ?-Sheaves on Reductive Groups -- Representations of Hecke Algebras and Characters of Symmetric Groups -- Dirac Cohomology for the Cubic Dirac Operator -- Double Crystal Graphs -- Induced Representations of
Affine Hecke Algebras and Canonical Bases of Quantum Groups -- A Pieri-Chevalley Type Formula for K(G/B) and Standard Monomial Theory -- Constructible Functions on Varieties Attached to Quivers -- On the Endomorphism Algebra of the
Steinberg Module -- Frobenius-Schur Functions -- A Generating Function for the Trace of the Iwahori-Hecke Algebra -- Quivers, Desingularizations and Canonical Bases -- Perverse Sheaves and Quantum Grothendieck Rings
ISBN:9781461200451
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics : 210
Keywords: Mathematics , Algebra , Group theory , Topological groups , Lie groups , Applied mathematics , Engineering mathematics , Mathematics , Topological Groups, Lie Groups , Algebra , Group Theory and Generalizations , Applications of Mathematics
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Call number:SPRINGER-2003-9781461200291:ONLINE Show nearby items on shelf
Title:The Orbit Method in Geometry and Physics In Honor of A.A. Kirillov
Author(s):
Date:2003
Size:1 online resource (474 p.)
Note:10.1007/978-1-4612-0029-1
Contents:A Principle of Variations in Representation Theory -- Finite Group Actions on Poisson Algebras -- Representations of Quantum Tori and G-bundles on Elliptic Curves -- Dixmier Algebras for Classical Complex Nilpotent Orbits via
Kraft-Procesi Models I -- Brèves remarques sur l’oeuvre de A. A. Kirillov -- Gerbes of Chiral Differential Operators. III -- Defining Relations for the Exceptional Lie Superalgebras of Vector Fields -- Schur-Weyl Duality and
Representations of Permutation Groups -- Quantization of Hypersurface Orbital Varieties insln -- Generalization of a Theorem of Waldspurger to Nice Representations -- Two More Variations on the Triangular Theme -- The Generalized
Cayley Map from an Algebraic Group to its Lie Algebra -- Geometry ofGLn(?)at Infinity: Hinges, Complete Collineations, Projective Compactifications, and Universal Boundary -- Why Would Multiplicities be Log-Concave? -- Point Processes
Related to the Infinite Symmetric Group -- Some Toric Manifolds and a Path Integral -- Projective Schur Functions as Bispherical Functions on Certain Homogeneous Superspaces -- Maximal Subalgebras of the Classical Linear Lie
Superalgebras
ISBN:9781461200291
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics : 213
Keywords: Mathematics , Group theory , Differential geometry , Manifolds (Mathematics) , Complex manifolds , Physics , Mathematics , Group Theory and Generalizations , Differential Geometry , Manifolds and Cell Complexes (incl. Diff.Topology) , Theoretical, Mathematical and Computational Physics
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Call number:SPRINGER-2003-9780857294289:ONLINE Show nearby items on shelf
Title:Basic Algebra Groups, Rings and Fields
Author(s): P. M Cohn
Date:2003
Size:1 online resource (465 p.)
Note:10.1007/978-0-85729-428-9
Contents:1. Sets -- 2. Groups -- 3. Lattices and Categories -- 4. Rings and Modules -- 5. Algebras -- 6. Multilinear Algebra -- 7. Field Theory -- 8. Quadratic Forms and Ordered Fields -- 9. Valuation Theory -- 10. Commutative Rings -- 11.
Infinite Field Extensions -- List of Notations -- Author Index
ISBN:9780857294289
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Group theory , Mathematics , Algebra , Group Theory and Generalizations
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
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