Complex Semisimple Quantum Groups and Representation Theory

✍ Scribed by Christian Voigt, Robert Yuncken

• Publisher: Springer International Publishing;Springer
• Year: 2020
• Tongue: English
• Leaves: 382
• Series: Lecture Notes in Mathematics 2264
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-x
Introduction (Christian Voigt, Robert Yuncken)....Pages 1-4
Multiplier Hopf Algebras (Christian Voigt, Robert Yuncken)....Pages 5-23
Quantized Universal Enveloping Algebras (Christian Voigt, Robert Yuncken)....Pages 25-193
Complex Semisimple Quantum Groups (Christian Voigt, Robert Yuncken)....Pages 195-233
Category ( \mathcal {O} ) (Christian Voigt, Robert Yuncken)....Pages 235-286
Representation Theory of Complex Semisimple Quantum Groups (Christian Voigt, Robert Yuncken)....Pages 287-356
Back Matter ....Pages 357-376

✦ Subjects

Mathematics; Group Theory and Generalizations; Functional Analysis; Topological Groups, Lie Groups; Associative Rings and Algebras; Abstract Harmonic Analysis