Hochschild Cohomology and Periodicity of Tame Weakly Symmetric Algebras

In this thesis we study the second Hochschild cohomology group of all tame weakly symmetric algebras having simply connected Galois coverings and only periodic modules. These algebras have been determined up to Morita equivalence by Białkowski, Holm and Skowroński in [4] where they give finite dimensional algebras A1(λ),A2(λ),A3,...A16 which are a full set of representatives of the equivalence classes. Hochschild cohomology is invariant under Morita equivalence, and this thesis describes HH²(Λ) for each algebra Λ = A1(λ),A2(λ),A3,…,A16 in this list. We also find the periodicity of the simple modules for each of these algebras. Moreover, for the algebra A1(λ) we find the minimal projective bimodule resolution of A1(λ) and discuss the periodicity of this resolution.