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Author Kharchenko, Vladislav, author
Title Quantum lie theory : a multilinear approach / by Vladislav Kharchenko
Imprint Cham : Springer International Publishing : Imprint: Springer, 2015
book jacket
Descript 1 online resource (xiii, 302 pages) : illustrations, digital ; 24 cm
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Series Lecture notes in mathematics, 0075-8434 ; 2150
Lecture notes in mathematics ; 2150
Note 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
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
Host Item Springer eBooks
Subject Lie algebras
Quantum theory
Associative Rings and Algebras
Non-associative Rings and Algebras
Group Theory and Generalizations
Quantum Physics
Alt Author SpringerLink (Online service)
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