Cyclic cohomology of Hopf algebras, and a non-commutative Chern-Weil theory

Abstract

We give a construction of ConnesMoscovicis cyclic cohomology for any Hopf algebra equipped with a character Furthermore we introduce a noncommutative Weil complex which connects the work of Gelfand and Smirnov with cyclic cohomology We show how the Weil complex arises naturally when looking at Hopf algebra actions and invariant higher traces to give a noncommutative version of the usual ChernWeil theory