Complex Semisimple Quantum Groups and Representation Theory

Christian / Yuncken Voigt - Collection Yellow Sale 2023

376 pages, parution le 24/09/2020

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Résumé

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.

- Introduction. - Multiplier Hopf Algebras. - Quantized Universal Enveloping Algebras. - Complex Semisimple Quantum Groups. - Category O. - Representation Theory of Complex Semisimple Quantum Groups.

Christian Voigt is a Senior Lecturer at the School of Mathematics, University of Glasgow. His main research area is noncommutative geometry, with a focus on quantum groups, operator K-theory, and cyclic homology.

Robert Yuncken is Maitre de Conferences at the Laboratoire de Mathematiques Blaise Pascal, Univerite Clermont Auvergne in France. His main research interests are in operator algebras, geometry, and representation theory.