Complex Semisimple Quantum Groups and Representation Theory / by Christian Voigt, Robert Yuncken.
2020
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Title
Complex Semisimple Quantum Groups and Representation Theory / by Christian Voigt, Robert Yuncken.
Edition
1st ed. 2020.
ISBN
9783030524630
3030524639
3030524620
9783030524623
3030524639
3030524620
9783030524623
Published
Cham : Springer International Publishing, 2020 ; Imprint Springer.
Language
English
Description
1 online resource (x, 376 pages) : illustrations.
Item Number
10.1007/978-3-030-52
Dewey Decimal Classification
512.2
Summary
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. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.
Access Note
Access limited to authorized users.
Series
Lecture Notes in Mathematics, 0075-8434 ; 2264.
Available in Other Form
Print version: 9783030524623
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