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.
- ISBN13 9783030524623
- Publish Date 25 September 2020
- Publish Status Active
- Publish Country CH
- Imprint Springer Nature Switzerland AG
- Edition 1st ed. 2020
- Format Paperback
- Pages 376
- Language English