Complex Semisimple Quantum Groups and Representation Theory

By Christian Voigt and Robert Yuncken

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 Poincar -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.

• Format: Paperback
• Language: English
• ISBN: 3030524620
• ISBN13: 9783030524623
• Release Date: September 2020
• Publisher: Springer
• Length: 376 Pages
• Weight: 1.19 lbs.
• Dimensions: 0.8" x 6.1" x 9.2"