國立高雄大學圖資館 |

Language: English

Back

Quantum lie theorya multilinear appr...

Kharchenko, Vladislav.

Quantum lie theorya multilinear approach /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quantum lie theoryby 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.
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 theorya 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 ;2035..

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:

191078
Lie algebras.

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

Dewey Class. No.: 512.482

Quantum lie theorya multilinear approach /
LDR:02237nmm a2200325 a 4500 001 477748
003 DE-He213
005 20160512110847.0
006 m d
007 cr nn 008maaau
008 160614s2015 gw s 0 eng d
020 $a 9783319227047$q(electronic bk.)
020 $a 9783319227030$q(paper)
024 7 $a 10.1007/978-3-319-22704-7 $2 doi
035 $a 978-3-319-22704-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA252.3 $b .K43 2015
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 512.482 $2 23
090 $a QA252.3 $b .K45 2015
100 1 $a Kharchenko, Vladislav. $3 732775
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 191078
650 0 $a Quantum theory. $3 199020
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Non-associative Rings and Algebras. $3 274087
650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Quantum Physics. $3 275010
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-22704-7
950 $a Mathematics and Statistics (Springer-11649)