Deformed mesh algebras of Dynkin type ℂₙ

@article{JerzyBiałkowski2012,
abstract = {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 of simple plane curve singularities of type $_\{2n-1\}$. Moreover, we describe the minimal (periodic) bimodule projective resolutions of the canonical mesh algebras of type ℂₙ.},
author = {Jerzy Białkowski, Karin Erdmann, Andrzej Skowroński},
journal = {Colloquium Mathematicae},
keywords = {mesh algebras; syzygies; periodic algebras; simple plane curve singularities; Cohen-Macaulay modules; stable Auslander algebras; deformed preprojective algebras; projective resolutions},
language = {eng},
number = {2},
pages = {217-230},
title = {Deformed mesh algebras of Dynkin type ℂₙ},
url = {http://eudml.org/doc/286681},
volume = {126},
year = {2012},
}

TY - JOUR
AU - Jerzy Białkowski
AU - Karin Erdmann
AU - Andrzej Skowroński
TI - Deformed mesh algebras of Dynkin type ℂₙ
JO - Colloquium Mathematicae
PY - 2012
VL - 126
IS - 2
SP - 217
EP - 230
AB - 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 of simple plane curve singularities of type $_{2n-1}$. Moreover, we describe the minimal (periodic) bimodule projective resolutions of the canonical mesh algebras of type ℂₙ.
LA - eng
KW - mesh algebras; syzygies; periodic algebras; simple plane curve singularities; Cohen-Macaulay modules; stable Auslander algebras; deformed preprojective algebras; projective resolutions
UR - http://eudml.org/doc/286681
ER -