An Application of a Theorem of Sheila Brenner for Hochschild Extension Algebras of a Truncated Quiver Algebra

Abstract

Let A be a truncated quiver algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of A is zero in A. We give the number of the indecomposable direct summands of the middle term of an almost split sequence for a class of Hochschild extension algebras of A by the standard duality module D(A).