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.
Highlights
In this thesis we study the second Hochschild cohomology group HH2(A) of all finite dimensional self-injective algebras A of finite representation type over an algebraically closed field K
We study certain finite dimensional algebras A of tame representation type and find a non-zero element rj in HH2(A) and an associative deformation A^ of A
I give more details in Chapter 2; it is sufficient here to note that the following theorem is the main re sult of this thesis which is given in Theorem 11.10 in Chapter 11, and deals with every finite dimensional self-injective algebra of finite representation type over an algebraically closed field K
Summary
In this thesis we study the second Hochschild cohomology group HH2(A) of all finite dimensional self-injective algebras A of finite representation type over an algebraically closed field K. To study HH2(A) for all finite dimensional self-injective algebras of finite representation type over an algebraically closed field K , it is enough to study HH2(A) for the representatives of the derived equivalence classes. I give more details in Chapter 2; it is sufficient here to note that the following theorem is the main re sult of this thesis which is given in Theorem 11.10, and deals with every finite dimensional self-injective algebra of finite representation type over an algebraically closed field K. We intend to look at the classification in [7] of finite dimensional self-injective one parametric of finite representation type tame weakly symmetric alge bras
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