Complex semisimple quantum groups and representation theory
Author(s)
Bibliographic Information
Complex semisimple quantum groups and representation theory
（Lecture notes in mathematics, v. 2264）
Springer, c2020
Available at / 31 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||2264200040918533
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Note
Includes bibliographical references (p. 371-374)
Description and Table of Contents
Description
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 Poincare-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.
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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