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＜電子ブック＞
Quantum Lie Theory : A Multilinear Approach / by Vladislav Kharchenko
(Lecture Notes in Mathematics. ISSN:16179692 ; 2150)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
大きさ	XIII, 302 p : online resource
著者標目	*Kharchenko, Vladislav author SpringerLink (Online service)
件　名	LCSH:Associative rings LCSH:Associative algebras LCSH:Nonassociative rings LCSH:Group theory LCSH:Quantum physics FREE:Associative Rings and Algebras FREE:Non-associative Rings and Algebras FREE:Group Theory and Generalizations FREE:Quantum Physics
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-22704-7

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