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Quantum Lie Theory : A Multilinear Approach - Vladislav Kharchenko

Quantum Lie Theory

A Multilinear Approach

By: Vladislav Kharchenko

eText | 24 December 2015

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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.

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Non-FictionMathematicsAlgebraSciencePhysicsQuantum Physics & Quantum Mechanics & Quantum Field TheoryGroups & Group Theory

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