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 . 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 of simple plane curve singularities of type . Moreover, we describe the minimal (periodic) bimodule projective resolutions of the canonical mesh algebras of type ℂₙ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-2-6,
author = {Jerzy Bia\l kowski and Karin Erdmann and Andrzej Skowro\'nski},
title = {Deformed mesh algebras of Dynkin type Cn},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {217-230},
zbl = {1261.16020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-2-6}
}
Jerzy Białkowski; Karin Erdmann; Andrzej Skowroński. Deformed mesh algebras of Dynkin type ℂₙ. Colloquium Mathematicae, Tome 126 (2012) pp. 217-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-2-6/