Overview
- First comprehensive treatment of quantum groups in the sense of Woronowicz
- Contains exercises with comments to help the reader deepen their knowledge of the subject
- Includes a detailed discussion of the representation theory of free orthogonal and unitary quantum groups
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Table of contents (16 chapters)
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Front Matter
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Quantum Groups
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Front Matter
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Quantum Rotations
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Front Matter
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Quantum Permutations
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Front Matter
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Advanced Topics
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Front Matter
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Keywords
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Introduction to Quantum Groups
Authors: Teo Banica
DOI: https://doi.org/10.1007/978-3-031-23817-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-23816-1Published: 02 January 2023
Softcover ISBN: 978-3-031-23819-2Published: 03 January 2024
eBook ISBN: 978-3-031-23817-8Published: 01 January 2023
Edition Number: 1
Number of Pages: X, 425
Number of Illustrations: 1 b/w illustrations
Topics: Mathematics, general, Operator Theory