On Cyclic Cohomology of ×-Hopf algebras

Abstract

In this paper we study the cyclic cohomology of certain -Hopf algebras: universal enveloping algebras, quantum algebraic tori, the Connes-Moscovici -Hopf algebroids and the Kadison bialgebroids. Introducing their stable anti Yetter-Drinfeld modules and cocyclic modules, we compute their cyclic cohomology. Furthermore, we provide a pairing for the cyclic cohomology of -Hopf algebras which generalizes the Connes-Moscovici characteristic map to -Hopf algebras. This enables us to transfer the -Hopf algebra cyclic cocycles to algebra cyclic cocycles.