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)

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Publisher's URL: http://dx.doi.org/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, Dr 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

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