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, (doi: 10.1093/imrn/rnaa370) (Early Online Publication)

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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:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Voigt, Dr 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 (OUP)
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 2021
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
309470Quantum groups in actionChristian VoigtEngineering and Physical Sciences Research Council (EPSRC)EP/T03064X/1M&S - Mathematics