Complex Semisimple Quantum Groups and Representation Theory

By: Christian Voigt, Robert Yuncken

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Paperback | 25 September 2020

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388 Pages

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23.5 x 15.5 x 2.54

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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.

Industry Reviews

"The book is largely self-contained. ... It is highly recommended for mathematicians of all levels wishing to learn about these topics, in the algebraic setting and/or in the analytic setting." (Huafeng Zhang, zbMATH 1514.20006, 2023)

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