Abstract
In this paper we study the second Hochschild cohomology group
HH
2
(
Λ
)
of a finite dimensional algebra
Λ. In particular, we determine
HH
2
(
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
HH
2
(
Λ
)
in the few cases where it is not zero.