Vanishing of the Hochschild cohomology for some self-injective special   biserial algebra of rank four
  In this paper, we determine the dimensions of the Hochschild cohomology groups of some self-injective special biserial algebra whose Grothendieck group is of rank $4$. This result provides us with a negative answer to Happel's question in [H]. 
Takahiko Furuya and Takao Hayami
math.RT