Deformed mesh algebras of Dynkin type $\mathbb{C}_n$

Jerzy Białkowski ¹   ; Karin Erdmann ²   ; Andrzej Skowroński ¹

¹ Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
² Mathematical Institute University of Oxford Oxford OX1 3LB, United Kingdom

Colloquium Mathematicum, Tome 126 (2012) no. 2, pp. 217-230

Résumé

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 $\mathbb C_n$.

Détail

DOI : 10.4064/cm126-2-6

Keywords: recent paper nbsp algebra prove deformed preprojective algebras generalized dynkin type mathbb sense earlier work trans amer math soc exactly isomorphism stable auslander algebras simple plane singularities dynkin type mathbb article complete picture showing deformed mesh algebras dynkin type mathbb isomorphic canonical mesh algebras type mathbb hence stable auslander algebras simple plane curve singularities type mathbb n moreover describe minimal periodic bimodule projective resolutions canonical mesh algebras type mathbb