Tate-Hochschild cohomology of Frobenius algebras

13 October 2011
Petter Bergh
This is based on joint work with Dave Jorgensen. Given a Gorenstein algebra, one can define Tate-Hochschild cohomology groups. These are defined for all degrees, non-negative as well as negative, and they agree with the usual Hochschild cohomology groups for all degrees larger than the injective dimension of the algebra. We prove certain duality theorems relating the cohomology groups in positive degree to those in negative degree, in the case where the algebra is Frobenius (for example symmetric). We explicitly compute all Tate-Hochschild cohomology groups for certain classes of Frobenius algebras, namely, certain quantum complete intersections.
  • Representation Theory Seminar