Deformed mesh algebras of Dynkin type ℂₙ

• Autorzy: Jerzy Białkowski , Karin Erdmann , Andrzej Skowroński
• Języki publikacji: EN

Abstrakty

EN

In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type 𝕃ₙ (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 $𝔸_{2n}$. 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 $𝔸_{2n-1}$. Moreover, we describe the minimal (periodic) bimodule projective resolutions of the canonical mesh algebras of type ℂₙ.

Kategorie tematyczne

• 16G50: Cohen-Macaulay modules
• 14H20: Singularities, local rings
• 16D50: Injective modules, self-injective rings
• 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 126
• Numer: 2
• Strony: 217-230

Daty

wydano

2012

Twórcy

autor

Jerzy Białkowski

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

autor

Karin Erdmann

• Mathematical Institute, University of Oxford, Oxford OX1 3LB, United Kingdom

autor

Andrzej Skowroński

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/cm126-2-6