Deformed mesh algebras of Dynkin type $\mathbb{C}_n$
Tom 126 / 2012
Streszczenie
In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type $\mathbb L_n$ (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 $\mathbb A_{2n}$. In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type $\mathbb C_n$ are isomorphic to the canonical mesh algebras of type $\mathbb C_n$, and hence to the stable Auslander algebras of simple plane curve singularities of type $\mathbb A_{2n-1}$. Moreover, we describe the minimal (periodic) bimodule projective resolutions of the canonical mesh algebras of type $\mathbb C_n$.
