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Quantum Lie Theory = A Multilinear Approach /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Quantum Lie Theory/ by Vladislav Kharchenko.
其他題名:	A Multilinear Approach /
作者:	Kharchenko, Vladislav.
面頁冊數:	XIII, 302 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Associative rings. -
電子資源:	https://doi.org/10.1007/978-3-319-22704-7
ISBN:	9783319227047

Quantum Lie Theory = A Multilinear Approach /
Kharchenko, Vladislav.

Quantum Lie TheoryA Multilinear Approach /[electronic resource] :by Vladislav Kharchenko. - 1st ed. 2015. - XIII, 302 p.online resource. - Lecture Notes in Mathematics,21500075-8434 ;. - Lecture Notes in Mathematics,2144.

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.

ISBN: 9783319227047

Standard No.: 10.1007/978-3-319-22704-7doiSubjects--Topical Terms:

893564
Associative rings.

LC Class. No.: QA251.5

Dewey Class. No.: 512.46

Quantum Lie Theory = A Multilinear Approach /
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