Equivariant Cyclic Cohomology of H-Algebras

Abstract

We define an equivariant $K_0$-theory for \textit{Yetter-Drinfeld} algebras over a Hopf algebra with an invertible antipode. We then show that this definition can be generalized to all Hopf-module algebras. We show that there exists a pairing, generalizing Connes' pairing, between this theory and a suitably defined Hopf algebra equivariant cyclic cohomology theory.

Final version to be published in "K-theory". The title has been changed, new examples added and it is shown that our K-theory is isomorphic to the K-theory defined in [14]