Hochschild cohomology for a class of some self-injective special biserial algebras of rank four

الأصل · EN

In this paper, we construct an explicit minimal projective bimodule resolution of a self-injective special biserial algebra Aₜ (T≥0) whose Grothendieck group is of rank 4. As a main result, we determine the dimension of the Hochschild cohomology group HHⁱ(Aₜ) of Aₜ for i≥0, completely. Moreover we give a presentation of the Hochschild cohomology ring modulo nilpotence HH*(Aₜ)/Nₐₜ of Aₜ by generators and relations in the case where T=0.