Overview
- Presents quantized coordinate ring as a main player dual to what is usually meant by quantum group in physics literature
- Illustrates quantization of the conventional Yang–Baxter and reflection equations, related to 3D integrability
- Leads to matrix product formulas for R and K matrices having intriguing applications
Part of the book series: Theoretical and Mathematical Physics (TMP)
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About this book
This book aims to present a unique approach to 3-dimensional integrability based on Aq. It starts from the tetrahedron equation, a 3-dimensional analogue of the Yang–Baxter equation, and its solution due to work by Kapranov–Voevodsky (1994).
Then, it guides readers to its variety of generalizations, relations to quantum groups, and applications. They include a connection to the Poincaré–Birkhoff–Witt basis of a unipotent part of Uq, reductions to the solutions of the Yang–Baxter equation, reflection equation, G2 reflection equation, matrix product constructions of quantum R matrices and reflection K matrices, stationary measures of multi-species simple-exclusion processes, etc.
These contents of the book are quite distinct from conventional approaches and will stimulate and enrich the theories of quantum groups and integrable systems.
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Keywords
Table of contents (18 chapters)
Reviews
“This book is well written, with numerous examples, bibliographical information, references, and pictures. Essentially, all of the computations are based around algebraic manipulations, and generally require no deep knowledge of representation theory, algebraic geometry, or integrable systems. … this is a very good book to move into the third dimension for studying integrable systems.” (Travis Scrimshaw, Mathematical Reviews, February, 2024)
Authors and Affiliations
Bibliographic Information
Book Title: Quantum Groups in Three-Dimensional Integrability
Authors: Atsuo Kuniba
Series Title: Theoretical and Mathematical Physics
DOI: https://doi.org/10.1007/978-981-19-3262-5
Publisher: Springer Singapore
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022
Hardcover ISBN: 978-981-19-3261-8Published: 26 September 2022
Softcover ISBN: 978-981-19-3264-9Published: 27 September 2023
eBook ISBN: 978-981-19-3262-5Published: 25 September 2022
Series ISSN: 1864-5879
Series E-ISSN: 1864-5887
Edition Number: 1
Number of Pages: XI, 331
Number of Illustrations: 64 b/w illustrations, 32 illustrations in colour
Topics: Mathematical Physics, Quantum Physics