Complex Semisimple Quantum Groups and Representation Theory

Voigt, C. and Yuncken, R. (2020) Complex Semisimple Quantum Groups and Representation Theory. Series: Lecture notes in mathematics, 2264. Springer. ISBN 9783030524623 (In Press)

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Publisher's URL: https://www.springer.com/gp/book/9783030524623

Abstract

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.

Item Type:Books
Status:In Press
Glasgow Author(s) Enlighten ID:Voigt, Dr Christian
Authors: Voigt, C., and Yuncken, R.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Publisher:Springer
ISBN:9783030524623

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