Complex Semisimple Quantum Groups and Representation Theory

1. Auflage 2020
ISBN: 978-3-030-52462-3
Verlag: Springer International Publishing

Buch, Englisch, Band 2264, 376 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 587 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Yuncken, Robert

Voigt, Christian

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

- Introduction. - Multiplier Hopf Algebras. - Quantized Universal Enveloping Algebras. - Complex Semisimple Quantum Groups. - Category O. - Representation Theory of Complex Semisimple Quantum Groups.

Über Autor(innen)

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.