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

Abstract

In this paper, we construct an explicit minimal projective bimodule resolution of a self-injective special biserial algebra $A_T$ ($T\ge 0$) whose Grothendieck group is of rank $4$. As a main result, we determine the dimension of the Hochschild cohomology group ${\mathrm{HH}}^i(A_T)$ of $A_T$ for $i\ge 0$, completely. Moreover we give a presentation of the Hochschild cohomology ring modulo nilpotence ${\mathrm{HH}}^{\ast }(A_T)/{\mathcal{N}}_{A_T}$ of $A_T$ by generators and relations in the case where $T=0$.

arXiv comment12 pages

References in corpus (1)

• Support varieties and the Hochschild cohomology ring modulo nilpotence