Vladislav Kharchenko: Quantum Lie Theory

Cover: 9783319227030 | Quantum Lie Theory | A Multilinear Approach | Vladislav Kharchenko

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Sprache: Englisch

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Beschreibung

This is an introduction to the mathematics behind the phrase ¿quantum Lie algebrä. 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.

Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2015
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiii 302 S.
ISBN-13:	9783319227030
ISBN-10:	3319227033
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Kharchenko, Vladislav
Auflage:	1st edition 2015
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 18 mm
Von/Mit:	Vladislav Kharchenko
Erscheinungsdatum:	25.12.2015
Gewicht:	0,487 kg