Quantum Lie Theory
Vladislav Kharchenko
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Springer International Publishing
Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
This is an introduction to the mathematics behind the phrase "e;quantum Lie algebra"e;. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary "e;quantum"e; 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.