Comparing the simplicial and the hochschild cohomologies of a finite dimensional algebra Original Research Article

Let A be a finite dimensional, basic algebra over an algebraically closed field k. We compare the Hochschild cohomology group Hi(A) = Hi(A, A) with the simplicial cohomology groups SHi(A, Z) defined in [6] for any abelian group Z. We show that SH1 (A,k+) is always a subspace of H1(A) and in case A is schurian SHi(A, k+) is a subspace of Hi(A) for i ≥ 1. We show several consequences of these results.