Cyclic cohomology and Baaj-Skandalis duality. Issue 1 (16th December 2013)

• Record Type: Journal Article
• Authors: Voigt, Christian
• Is Part Of: Journal of K-Theory. Volume 13:Issue 1(2014)
• Page Start: 115
• Page End: 145
• Publication Date: 2013-12-16
• Subjects: Cyclic Cohomology, -- Quantum Groups, -- Crossed Products; 19D55; K-theory -- Periodicals; 512.6605
• DOI: 10.1017/is013012001jkt248
• Languages: English
• ISSNs: 1865-2433

Abstract

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. 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.