Compact Matrix Quantum Groups and Their Combinatorics

The book presents the theory of compact quantum groups and its interactions with quantum information and graph theory and combinatorics.

Amaury Freslon (Author)

9781009345736, Cambridge University Press

Hardback, published 27 July 2023

300 pages
23.5 x 15.8 x 2.3 cm, 0.59 kg

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.

Preface. Part I. Getting Started: 1. Introducing quantum groups
2. Representation theory
Part II. Partitions Enter The Picture: 3. Partition quantum groups
4. The representation theory of partition quantum groups
5. Measurable and topological aspects
Part III. Further Examples And Applications: 6. A unitary excursion
7. Further examples
8. Back to the game
Appendix A
Appendix B
Appendix C.

Subject Areas: Algebra [PBF]