In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type ₙ (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane singularities of Dynkin type ${}_{2n}$. In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type ℂₙ are isomorphic to the canonical mesh algebras of type ℂₙ, and hence to the stable Auslander algebras...

We complete the derived equivalence classification of all weakly symmetric algebras of domestic type over an algebraically closed field, by solving the problem of distinguishing standard and nonstandard algebras up to stable equivalence, and hence derived equivalence. As a consequence, a complete stable equivalence classification of weakly symmetric algebras of domestic type is obtained.

Let $R⋉M$ be a trivial extension of a ring $R$ by an $R$-$R$-bimodule $M$ such that $M_R$, ${}_{R}M$, ${(R,0)}_{R⋉M}$ and ${}_{R⋉M}(R,0)$ have finite flat dimensions. We prove that $(X,\alpha )$ is a Ding projective left $R⋉M$-module if and only if the sequence $M{\otimes }_{R}M{\otimes }_{R}X\stackrel{M\otimes \alpha }{⟶}M{\otimes }_{R}X\stackrel{\alpha }{\to }X$ is exact and $\mathrm{coker}\left(\alpha \right)$ is a Ding projective left $R$-module. Analogously, we explicitly describe Ding injective $R⋉M$-modules. As applications, we characterize Ding projective and Ding injective modules over Morita context rings with zero bimodule homomorphisms.