Quantum Lie Theory / Lecture Notes in Mathematics Bd.2150 (PDF)
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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.
- Autor: Vladislav Kharchenko
- 2015, 1st ed. 2015, 302 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319227041
- ISBN-13: 9783319227047
- Erscheinungsdatum: 24.12.2015
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