Isomorphic trivial extensions of finite dimensional algebras

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