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Quantum lie theorya multilinear appr...

Kharchenko, Vladislav.

Quantum lie theorya multilinear approach /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Quantum lie theoryby Vladislav Kharchenko.
其他題名:	a multilinear approach /
作者:	Kharchenko, Vladislav.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xiii, 302 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Lie algebras.
電子資源:	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 /
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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.
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