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Quantum Lie Theory A Multilinear Approach
Author
Title
Quantum Lie Theory [electronic resource] : A Multilinear Approach / by Vladislav Kharchenko.
ISBN
9783319227047
Edition
1st ed. 2015.
Publication
Cham : Springer International Publishing : Imprint: Springer, 2015.
Physical Description
1 online resource (XIII, 302 p).
Local Notes
Access is available to the Yale community.
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Access restricted by licensing agreement.
Summary
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.
Variant and related titles
Springer ENIN.
Other formats
Printed edition:
Printed edition:
Format
Books / Online
Language
English
Added to Catalog
September 28, 2018
Series
Lecture Notes in Mathematics, 2150
Contents
Elements of noncommutative algebra
Poincar´e-Birkhoff-Witt basis
Quantizations of Kac-Moody algebras
Algebra of skew-primitive elements
Multilinear operations
Braided Hopf algebras
Binary structures
Algebra of primitive nonassociative polynomials.
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