Equivariant Poincaré duality for quantum group actions

Nest, R. and Voigt, C. (2010) Equivariant Poincaré duality for quantum group actions. Journal of Functional Analysis, 258(5), pp. 1466-1503. (doi: 10.1016/j.jfa.2009.10.015)

Abstract

We extend the notion of Poincar\'e duality in $ KK $-theory to the setting of quantum group actions. An important ingredient in our approach is the replacement of ordinary tensor products by braided tensor products. Along the way we discuss general properties of equivariant $ KK $-theory for locally compact quantum groups, including the construction of exterior products. As an example, we prove that the standard Podle\'s sphere is equivariantly Poincar\'e dual to itself.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Voigt, Professor Christian
• Authors: Nest, R., and Voigt, C.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Functional Analysis
• Publisher: Elsevier
• ISSN: 0022-1236
• ISSN (Online): 1096-0783
• Copyright Holders: Copyright © 2010 Elsevier
• First Published: First published in Journal of Functional Analysis 258(5):1466-1503
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher