On the extension-closed property for the subcategory $\text{Tr}(Ω^2({\rm mod}-A))$

Abstract

We present a monomial quiver algebra A having the property that the subcategory Tr(Ω 2 (mod −A)) is not extension-closed. This answers a question raised by Idun Reiten.and the relations are given by I = xy, yz, zx, x 3 . Let S i denote the simple