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

Volume 126 / 2012

Jerzy Białkowski, Karin Erdmann, Andrzej Skowroński Colloquium Mathematicum 126 (2012), 217-230 MSC: Primary 16D50, 16G50, 16G70, 14H20. DOI: 10.4064/cm126-2-6

Abstract

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 $\mathbb C_n$.

Authors

  • Jerzy BiałkowskiFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail
  • Karin ErdmannMathematical Institute
    University of Oxford
    Oxford OX1 3LB, United Kingdom
    e-mail
  • Andrzej SkowrońskiFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail

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