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Lecture Notes in Mathematics

Quantum Lie Theory

A Multilinear Approach

Authors: Kharchenko, Vladislav

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eBook 44,02 €
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  • ISBN 978-3-319-22704-7
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Softcover 54,99 €
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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.


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)


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook 44,02 €
price for China (P.R.) (gross)
  • ISBN 978-3-319-22704-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 54,99 €
price for China (P.R.) (gross)
  • ISBN 978-3-319-22703-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Quantum Lie Theory
Book Subtitle
A Multilinear Approach
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2150
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-22704-7
DOI
10.1007/978-3-319-22704-7
Softcover ISBN
978-3-319-22703-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIII, 302
Topics