Cyclic cohomology and multiplier Hopf algebras

Abstract

In this paper, we study cyclic cohomology theory on a regular multiplier Hopf algebra. Given a modular pair consisting of a group-like element, a character and in involution for a regular multiplier Hopf algebra, we associate a cyclic module. The approach is based on the Connes-Moscovici cyclic module of Hopf algebras and we obtain the same cyclic modules when our algebra has an identity.