Introduction to quantum groups / Teo Banica.
Banica, Teo, author.
2022
QC20.7.G76
Available Online

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Title Introduction to quantum groups / Teo Banica.
Author Banica, Teo, author.
ISBN 9783031238178 (electronic bk.)
3031238176 (electronic bk.)
9783031238161
DOI https://doi.org/10.1007/978-3-031-23817-8
Published Cham : Springer, 2022.
Language English
Description 1 online resource (x, 425 pages) : illustrations
Item Number 10.1007/978-3-031-23817-8 doi
Call Number QC20.7.G76
Dewey Decimal Classification 530.14/3
Summary This book introduces the reader to quantum groups, focusing on the simplest ones, namely the closed subgroups of the free unitary group. Although such quantum groups are quite easy to understand mathematically, interesting examples abound, including all classical Lie groups, their free versions, half-liberations, other intermediate liberations, anticommutation twists, the duals of finitely generated discrete groups, quantum permutation groups, quantum reflection groups, quantum symmetry groups of finite graphs, and more. The book is written in textbook style, with its contents roughly covering a one-year graduate course. Besides exercises, the author has included many remarks, comments and pieces of advice with the lone reader in mind. The prerequisites are basic algebra, analysis and probability, and a certain familiarity with complex analysis and measure theory. Organized in four parts, the book begins with the foundations of the theory, due to Woronowicz, comprising axioms, Haar measure, Peter-Weyl theory, Tannakian duality and basic Brauer theorems. The core of the book, its second and third parts, focus on the main examples, first in the continuous case, and then in the discrete case. The fourth and last part is an introduction to selected research topics, such as toral subgroups, homogeneous spaces and matrix models. Introduction to Quantum Groups offers a compelling introduction to quantum groups, from the simplest examples to research level topics.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed January 23, 2023).
Available in Other Form Introduction to Quantum Groups
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Part I. Quantum groups
Chapter 1. Quantum spaces
Chapter 2. Quantum groups
Chapter 3. Representation theory
Chapter 4. Tannakian duality
Part II. Quantum rotations
Chapter 5. Free rotations
Chapter 6. Unitary groups
Chapter 7. Easiness, twisting
Chapter 8. Probabilistic aspects
Part III. Quantum permutations
Chapter 9. Quantum permutations
Chapter 10. Quantum reflections
Chapter 11. Classification results
Chapter 12. The standard cube
Part IV. Advanced topics
Chapter 13. Toral subgroups
Chapter 14. Amenability, growth
Chapter 15. Homogeneous spaces
Chapter 16. Modelling questions
Bibliography
Index.

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