Connes' Pairings for a New K-Theory over Weak Hopf Algebras

Abstract

In this article we first study an equivariant cyclic cohomology for weak H-module agebras over a weak Hopf algebra H with a bijective antipode. Then we define an equivariant K-theory for weak quantum Yetter–Drinfeld algebras over H and establish a generalized Connes' pairing between the equivariant cyclic cohomology and the equivariant K-theory. As an application we consider our theory for groupoids.

Key Words:

• Connes' pairing
• Equivariant cyclic cohomology
• Weak Hopf algebra
• Weak module algebra

2010 Mathematics Subject Classification:

• 16W30

ACKNOWLEDGMENT

We thank the referee for the helpful comments. The work was partially supported by the NNSF of China (Nos. 10871042, 11261063) and the NSF of Jiangsu Province (No. BK2012736).

Notes

Communicated by J. Alev.