Equivariant cyclic homology for quantum groups

Abstract

We define equivariant periodic cyclic homology for bornological quantum groups. Generalizing corresponding results from the group case, we show that the theory is homotopy invariant, stable and satisfies excision in both variables. Along the way we prove Radford’s formula for the antipode of a bornological quantum group. Moreover we discuss anti-Yetter–Drinfeld modules and establish an analogue of the Takesaki–Takai duality theorem in the setting of bornological quantum groups.