On the Decomposition of the Hochschild Cohomology Group of a Monomial Algebra Satisfying a Separability Condition

Abstract

In this paper, we consider the finite connected quiver Q having two subquivers Q (1) and Q (2) with . Suppose that Q (i) is not a subquiver of Q (j) where {i, j} = {1, 2}. For a monomial algebra Λ =kQ/I obtained by the quiver Q, when the associated sequence of paths given by Minsharp <(I) satisfies a certain separability condition, we propose the method so that we easily construct a minimal projective resolution of Λ as a right Λ e -module and calculate the Hochschild cohomology group of Λ.