Zhengfang Wang (MPI Bonn), B-infinity algebra structure on Tate-Hochschild cohomology.

Abstract:

We first recall the notion of B-infinity algebra, which is in particular an A-infinity algebra. For instance, the Hochschild cochain complex of an associative algebra (more generally, an A-infinity algebra) has the structure of a B-infinity algebra.

Following Buchweitz, we define the Tate-Hochschild cohomology of an algebra as the Yoneda algebra of the identity bimodule in the singularity category of bimodules. In this talk, we construct a complex, called singular Hochschild cochain complex, to compute the Tate-Hochschild cohomology. We prove that there is a B-infinity algebra structure on the singular Hochschild cochain complex, by giving an explicit action of little 2-discs operad on this complex.