Complex semisimple quantum groups and representation theory
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 fi…
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- Full title :Complex semisimple quantum groups and representation theory / Christian Voigt, Robert Yuncken.
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.
Read More ↓Edition Statements
- Publication Date:2020.
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham
- Language:eng
- Publication Date:2020.
The Physical Object
- Description:1 online resource (x, 376 pages) : : illustrations
Edition Identifiers
- ISBN:9783030524630, 3030524639
- oclc:on1197837773
- LC Classification:QA174.2
- Dewey Decimal:512/.2
Table of Contents
Introduction. -- Multiplier Hopf Algebras. -- Quantized Universal Enveloping Algebras. -- Complex Semisimple Quantum Groups. -- Category O. -- Representation Theory of Complex Semisimple Quantum Groups.
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