Lecture Notes in Mathematics

Voigt, Christian; Yuncken, Robert

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 representationtheory 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.

Details

Published by: Springer

Publication Date: 2020-09-25

Format: Paperback

ISBN-13: 9783030524623

DOI: 10.1007/978-3-030-52463-0

Dimensions: 235cm x155cm

Pages: 376