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Quantum lie theory = a multilinear a...

Kharchenko, Vladislav.

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Quantum lie theory = a multilinear approach /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quantum lie theory/ by Vladislav Kharchenko.
Reminder of title:	a multilinear approach /
Author:	Kharchenko, Vladislav.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xiii, 302 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Lie algebras. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-22704-7
ISBN:	9783319227047$q(electronic bk.)

Quantum lie theory = a multilinear approach /
Kharchenko, Vladislav.

Quantum lie theorya multilinear approach /[electronic resource] :by Vladislav Kharchenko. - Cham :Springer International Publishing :2015. - xiii, 302 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21500075-8434 ;. - Lecture notes in mathematics ;2046..

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$q(electronic bk.)

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

526115
Lie algebras.

LC Class. No.: QA252.3 / .K43 2015

Dewey Class. No.: 512.482

Quantum lie theory = a multilinear approach /
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100 1 $a Kharchenko, Vladislav. $3 2165679
245 1 0 $a Quantum lie theory $h [electronic resource] : $b a multilinear approach / $c by Vladislav Kharchenko.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xiii, 302 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2150
505 0 $a 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.
520 $a 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.
650 0 $a Lie algebras. $3 526115
650 0 $a Quantum theory. $3 516552
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Associative Rings and Algebras. $3 897405
650 2 4 $a Non-associative Rings and Algebras. $3 891108
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Quantum Physics. $3 893952
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Lecture notes in mathematics ; $v 2046. $3 1534285
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-22704-7
950 $a Mathematics and Statistics (Springer-11649)