Self-injective algebras and the second Hochschild cohomology group

In this paper we study the second Hochschild cohomology group HH2(Λ) of a finite dimensional algebra Λ. In particular, we determine HH2(Λ) where Λ is a finite dimensional self-injective algebra of finite representation type over an algebraically closed field K and show that this group is zero for most such Λ; we give a basis for HH2(Λ) in the few cases where it is not zero.