On the assembly map for complex semisimple quantum groups

Voigt, C. (2022) On the assembly map for complex semisimple quantum groups. International Mathematics Research Notices, 2022(13), pp. 9603-9632. (doi: 10.1093/imrn/rnaa370)

Abstract

We show that complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups, satisfy a categorical version of the Baum–Connes conjecture with trivial coefficients. Our approach, based on homological algebra in triangulated categories, is compatible with the previously studied deformation picture of the assembly map and allows us to define an assembly map with arbitrary coefficients for these quantum groups.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Voigt, Professor Christian
• Authors: Voigt, C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Mathematics Research Notices
• Publisher: Oxford University Press
• ISSN: 1073-7928
• ISSN (Online): 1687-0247
• Published Online: 08 February 2021
• Copyright Holders: Copyright © 2021 The Authors
• First Published: First published in International Mathematics Research Notices 2022(13): 9603-9632
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
309470		Quantum groups in action	Christian Voigt	Engineering and Physical Sciences Research Council (EPSRC)	EP/T03064X/1	M&S - Mathematics