Compact Matrix Quantum Groups and Their Combinatorics

Amaury Freslon

doi:10.1017/9781009345705

An organised step-by-step introduction to the theory of compact quantum groups, starting with examples coming from quantum physics, which stems from the basic undergraduate mathematics curriculum. Introducing more abstract concepts along the way when needed, the reader is led from the fundamentals of the theory to recent research results. The emphasis is put on the combinatorics underlying compact quantum groups, which is very elementary to describe but leads to profound results. This book includes many exercises to help students work through new concepts and ideas and consolidate their understanding. The theory itself is illustrated by an array of examples, some related to other fields of Mathematics such as free probability theory or graph theory. The book is intended for graduate students, motivated undergraduate students and researchers.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-xii
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Part I - Getting Started
pp 1-2
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1 - Introducing Quantum Groups
pp 3-31
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2 - Representation Theory
pp 32-58
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Part II - Partitions Enter The Picture
pp 59-60
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3 - Partition Quantum Groups
pp 61-90
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4 - The Representation Theory of Partition Quantum Groups
pp 91-114
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5 - Measurable and Topological Aspects
pp 115-146
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Part III - Further Examples and Applications
pp 147-148
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6 - A Unitary Excursion
pp 149-182
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7 - Further Examples
pp 183-220
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8 - Back to the Game
pp 221-263
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Appendix A - Two Theorems on Complex Matrix Algebras
pp 264-266
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Appendix B - Classical Compact Matrix Groups
pp 267-270
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Appendix C - General Compact Quantum Groups
pp 271-281
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References
pp 282-285
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Index
pp 286-288
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Compact Matrix Quantum Groups and Their Combinatorics

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-xii

Part I - Getting Started
pp 1-2

1 - Introducing Quantum Groups
pp 3-31

2 - Representation Theory
pp 32-58

Part II - Partitions Enter The Picture
pp 59-60

3 - Partition Quantum Groups
pp 61-90

4 - The Representation Theory of Partition Quantum Groups
pp 91-114

5 - Measurable and Topological Aspects
pp 115-146

Part III - Further Examples and Applications
pp 147-148

6 - A Unitary Excursion
pp 149-182

7 - Further Examples
pp 183-220

8 - Back to the Game
pp 221-263

Appendix A - Two Theorems on Complex Matrix Algebras
pp 264-266

Appendix B - Classical Compact Matrix Groups
pp 267-270

Appendix C - General Compact Quantum Groups
pp 271-281

References
pp 282-285

Index
pp 286-288

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Compact Matrix Quantum Groups and Their Combinatorics

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