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Complex semisimple quantum groups and representation theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Complex semisimple quantum groups and representation theoryby Christian Voigt, Robert Yuncken.
Author:	Voigt, Christian.
other author:	Yuncken, Robert.
Published:	Cham :Springer International Publishing :2020.
Description:	x, 376 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Group theory.
Online resource:	https://doi.org/10.1007/978-3-030-52463-0
ISBN:	9783030524630$q(electronic bk.)

Complex semisimple quantum groups and representation theory
Voigt, Christian.

Complex semisimple quantum groups and representation theory[electronic resource] /by Christian Voigt, Robert Yuncken. - Cham :Springer International Publishing :2020. - x, 376 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v.22640075-8434 ;. - Lecture notes in mathematics ;2035..

This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincare-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.

ISBN: 9783030524630$q(electronic bk.)

Standard No.: 10.1007/978-3-030-52463-0doiSubjects--Topical Terms:

189579
Group theory.

LC Class. No.: QA174.2

Dewey Class. No.: 512.2

Complex semisimple quantum groups and representation theory
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520 $a This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincare-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.
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