Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2150)
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About this book
This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
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Table of contents (8 chapters)
Reviews
“The contents of the chapters 2-8 are mostly based on papers of the author and are here presented as a unified, self-contained whole with the first chapter containing the necessary preliminaries, making the exposition more accessible to a broader audience. … Each chapter ends with detailed notes providing pointers to literature and some open questions related to the presented material are discussed as well.” (Isar Rober Goyvaerts, zbMATH 1337.17001, 2016)
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Bibliographic Information
Book Title: Quantum Lie Theory
Book Subtitle: A Multilinear Approach
Authors: Vladislav Kharchenko
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-22704-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-22703-0Published: 25 December 2015
eBook ISBN: 978-3-319-22704-7Published: 24 December 2015
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIII, 302
Topics: Associative Rings and Algebras, Non-associative Rings and Algebras, Group Theory and Generalizations, Quantum Physics