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.Comment: Corrections to some calculation