Let $A$ be an ADE-hypersurface singularity in dimension one. For example in Dynkin type $A_n$, A is given by $K[[x,y]]/(x^2+y^{n+1})$.

Then $A$ is CM-finite and let $M$ be the direct sum of all indecomposable maximal CM-modules of $A$ and $B=\underline{End_A}(M)$ the stable endomorphism ring of $M$.

Question: Is there a description by quiver and relations of $B$ depending on the Dynkin type somwhere?

It should be a finite dimensional quiver algebra but I was not able to find a reference for the explicit description, while in dimension two it leads to the famous preprojective algebras. Im especially interested in the cases of $A_n$ (there the algebra is a preprojective algebra when $n$ is odd?) and $E_6$.


I found the answer in theorem 8.7 in the survey article on periodic algebras by Erdmann and Skowronski. They are certain (twisted) mesh algebras of Dynkin type.


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