Part of Encyclopedia of Mathematics and its Applications
Product details
Publication planned for: April 2018
format: Multiple copy pack
isbn: 9781108679077
dimensions: 234 x 156 mm
availability: Not yet published - available from April 2018
This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. The first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand?Naimark and Vidav Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive bibliography.
Volume 1: Preface
1. Foundations
2. Beginning the proof of the non-associative Vidav Palmer theorem
3. Concluding the proof of the non-associative Vidav Palmer theorem
4. Jordan spectral theory
References
Symbol index
Subject index.
Volume 2: Preface
5. Non-commutative JBW*-algebras, JB*-triples revisited, and a unit-free Vidav Palmer type non-associative theorem
6. Representation theory for non-commutative JB*-algebras and alternative C*-algebras
7. Zel'manov approach
8. Selected topics in the theory of non-associative normed algebras
Reference Papers
References Books
Symbol index for Volume 2
Subject index for Volume 2
Symbol index for Volume 1
Subject index for Volume 1.
Part of Australian Mathematical Society Lecture Series
Product details
Publication planned for: April 2018
format: Paperback
isbn: 9781108441940
dimensions: 228 x 152 mm
contains: 25 b/w illus.
availability: Not yet published - available from April 2018
There are a number of intriguing connections between Painleve equations and orthogonal polynomials, and this book is one of the first to provide an introduction to these. Researchers in integrable systems and non-linear equations will find the many explicit examples where Painleve equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painleve transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painleve equations are worked out in detail, with a survey of recent results and an outline of their close relationship with orthogonal polynomials. Exercises throughout the book help the reader to get to grips with the material. The author is a leading authority on orthogonal polynomials, giving this work a unique perspective on Painleve equations.
1. Introduction
2. Freud weights and discrete Painleve I
3. Discrete Painleve II
4. Ladder operators
5. Other semi-classical orthogonal polynomials
6. Special solutions of Painleve equations
7. Asymptotic behavior of orthogonal polynomials near critical points
Appendix. Solutions to exercises
References
Index.
Part of London Mathematical Society Student Texts
Product details
Publication planned for: May 2018
format: Hardback
isbn: 9781107101364
format: Paperback
isbn: 9781107499027
dimensions: 228 x 152 mm
availability: Not yet published - available from May 2018
The notion of an (∞,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This book provides a relatively self-contained source of the definitions of the different models, the model structure (homotopy theory) of each, and the equivalences between the models. While most of the current literature focusses on how to extend category theory in this context, and centers in particular on the quasi-category model, this book offers a balanced treatment of the appropriate model structures for simplicial categories, Segal categories, complete Segal spaces, quasi-categories, and relative categories, all from a homotopy-theoretic perspective. Introductory chapters provide background in both homotopy and category theory and contain many references to the literature, thus making the book accessible to graduates and to researchers in related areas.
Preface
Acknowledgments
Introduction
1. Models for homotopy theories
2. Simplicial objects
3. Topological and categorical motivation
4. Simplicial categories
5. Complete Segal spaces
6. Segal categories
7. Quasi-categories
8. Relative categories
9. Comparing functors to complete Segal spaces
10. Variants on (∞, 1)-categories
References
Index.
Part of Cambridge Studies in Advanced Mathematics
Product details
Publication planned for: June 2018
format: Hardback
isbn: 9781107182332
dimensions: 228 x 152 mm
availability: Not yet published - available from June 2018
This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.
Part I. Finite Abelian Groups and the DFT:
1. Finite Abelian groups
2. The Fourier transform on finite Abelian groups
3. Dirichlet's theorem on primes in arithmetic progressions
4. Spectral analysis of the DFT and number theory
5. The fast Fourier transform
Part II. Finite Fields and Their Characters:
6. Finite fields
7. Character theory of finite fields
Part III. Graphs and Expanders:
8. Graphs and their products
9. Expanders and Ramanujan graphs
Part IV. Harmonic Analysis of Finite Linear Groups:
10. Representation theory of finite groups
11. Induced representations and Mackey theory
12. Fourier analysis on finite affine groups and finite Heisenberg groups
13. Hecke algebras and multiplicity-free triples
14. Representation theory of GL(2,Fq).
Part of London Mathematical Society Student Texts
Product details
Publication planned for: June 2018
format: Hardback
isbn: 9781108425902
dimensions: 228 x 152 mm
contains: 12 exercises
availability: Not yet published - available from June 2018
This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.
Introduction
6. Blocks and source algebras
7. Modules over finite p-groups
8. Local structure
9. Isometries and bimodules
10. Structural results in block theory
11. Blocks with cyclic defect groups
12. Blocks with Klein four defect groups
Appendix
References
Index.