Isomorphic trivial extensions of finite dimensional algebras

Let Λ be a finite dimensional algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of Λ is zero in Λ. Let T(Λ)=Λtimes sign, left closedD(Λ) be the trivial extension of Λ by its minimal injective cogenerator D(Λ). We characterize, in terms of quivers and relations, the algebras Λ′ such that T(Λ)similar, equalsT(Λ′).