Overview
- Provides a comprehensive, accessible and self-contained introduction to the theory of quantized universal enveloping algebras and their associated quantized semisimple Lie groups
- Presents complete proofs of many results that are otherwise scattered throughout the literature
- Offers a unified approach to both the algebraic and the analytic theory of quantum groups using coherent conventions and notations
- The first book to address the representation theory of general complex semisimple quantum groups
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2264)
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Table of contents (6 chapters)
Keywords
About this book
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 representationtheory 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.
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Authors and Affiliations
About the authors
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 Maître de Conférences at the Laboratoire de Mathématiques Blaise Pascal, Univerité Clermont Auvergne in France. His main research interests are in operator algebras, geometry, and representation theory.
Bibliographic Information
Book Title: Complex Semisimple Quantum Groups and Representation Theory
Authors: Christian Voigt, Robert Yuncken
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-52463-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-52462-3Published: 25 September 2020
eBook ISBN: 978-3-030-52463-0Published: 24 September 2020
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 376
Number of Illustrations: 25 b/w illustrations
Topics: Group Theory and Generalizations, Functional Analysis, Topological Groups, Lie Groups, Associative Rings and Algebras, Abstract Harmonic Analysis