Complex Semisimple Quantum Groups and Representation Theory

di Christian Voigt (Autore)

Robert Yuncken (Autore)

Springer Nature Switzerland AG, 2020

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.

• Autore: Christian Voigt, Robert Yuncken
• Editore: Springer Nature Switzerland AG
• Collana: Lecture Notes in Mathematics
• Anno: 2020
• Rilegatura: Paperback / softback
• Pagine: 376 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783030524623

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