Complex Semisimple Quantum Groups and Representation Theory

von Christian Voigt, Robert Yuncken

376 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783030524623
• Sprache: Englisch
• Erscheinungsdatum: 25.09.2020
• Genre: Mathematik/Arithmetik, Algebra
• Verlag: Springer International Publishing