Cyclic cohomology and Baaj-Skandalis duality

Voigt, C. (2014) Cyclic cohomology and Baaj-Skandalis duality. Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology, 13(1), pp. 115-145. (doi: 10.1017/is013012001jkt248)

Abstract

We construct a duality isomorphism in equivariant periodic cyclic homology analogous to Baaj-Skandalis duality in equivariant Kasparov theory. As a consequence we obtain general versions of the Green-Julg theorem and the dual Green-Julg theorem in periodic cyclic theory.<p></p> Throughout we work within the framework of bornological quantum groups, thus in particular incorporating at the same time actions of arbitrary classical Lie groups as well as actions of compact or discrete quantum groups. An important ingredient in the construction of our duality isomorphism is the notion of a modular pair for a bornological quantum group, closely related to the concept introduced by Connes and Moscovici in their work on cyclic cohomology for Hopf algebras.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Voigt, Professor Christian
• Authors: Voigt, C.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology
• Publisher: Cambridge University Press
• ISSN: 1865-2433
• ISSN (Online): 1865-5394
• Copyright Holders: Copyright © 2014 ISOPP
• First Published: First published in the Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology 13(1):115-145
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher