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
  Aomori
  Iwate
  Miyagi
  Akita
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  Ibaraki
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||2264200040918533
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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