Stable anti-Yetter–Drinfeld modules

Abstract

We define and study a class of entwined modules (stable anti-Yetter–Drinfeld modules) that serve as coefficients for the Hopf-cyclic homology and cohomology. In particular, we explain their relationship with Yetter–Drinfeld modules and Drinfeld doubles. Among sources of examples of stable anti-Yetter–Drinfeld modules, we find Hopf–Galois extensions with a flipped version of the Miyashita–Ulbrich action. To cite this article: P.M. Hajac et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).