Title Complex semisimple quantum groups and representation theory / Christian Voigt, Robert Yuncken

Published Cham : Springer, 2020

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Description 1 online resource (x, 376 pages) : illustrations Series Lecture Notes in Mathematics, 0075-8434 ; 2264 Lecture notes in mathematics (Springer-Verlag) ; 2264. 0075-8434 Contents Introduction. -- Multiplier Hopf Algebras. -- Quantized Universal Enveloping Algebras. -- Complex Semisimple Quantum Groups. -- Category O. -- Representation Theory of Complex Semisimple Quantum Groups Summary 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 Poincaré-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 Bibliography Includes bibliographical references Notes Online resource; title from PDF title page (SpringerLink, viewed November 19, 2020) Subject Group theory. Functional analysis. Topological groups. Lie groups. Associative rings. Rings (Algebra) Harmonic analysis. Fourier Analysis Teoría de grupos Anillos (Álgebra) Associative rings Functional analysis Group theory Harmonic analysis Lie groups Rings (Algebra) Topological groups Form Electronic book Author Yuncken, Robert ISBN 9783030524630 3030524639

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