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2010 Gentle algebras arising from surface triangulations
Ibrahim Assem, Thomas Brüstle, Gabrielle Charbonneau-Jodoin, Pierre-Guy Plamondon
Algebra Number Theory 4(2): 201-229 (2010). DOI: 10.2140/ant.2010.4.201

Abstract

We associate an algebra A(Γ) to a triangulation Γ of a surface S with a set of boundary marking points. This algebra A(Γ) is gentle and Gorenstein of dimension one. We also prove that A(Γ) is cluster-tilted if and only if it is cluster-tilted of type A or A ̃, or if and only if the surface S is a disc or an annulus. Moreover all cluster-tilted algebras of type A or A ̃ are obtained in this way.

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Ibrahim Assem. Thomas Brüstle. Gabrielle Charbonneau-Jodoin. Pierre-Guy Plamondon. "Gentle algebras arising from surface triangulations." Algebra Number Theory 4 (2) 201 - 229, 2010. https://doi.org/10.2140/ant.2010.4.201

Information

Received: 8 April 2009; Revised: 24 June 2009; Accepted: 6 August 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1242.16011
MathSciNet: MR2592019
Digital Object Identifier: 10.2140/ant.2010.4.201

Subjects:
Primary: 16S99
Secondary: 16G20 , 57M50 , 57N05

Keywords: bordered surface with marked points , gentle algebra , quiver with potential , triangulated surface

Rights: Copyright © 2010 Mathematical Sciences Publishers

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