Vol. 4, No. 2, 2010

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Gentle algebras arising from surface triangulations

Ibrahim Assem, Thomas Brüstle, Gabrielle Charbonneau-Jodoin and Pierre-Guy Plamondon

Vol. 4 (2010), No. 2, 201–229
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.

Keywords
bordered surface with marked points, triangulated surface, quiver with potential, gentle algebra
Mathematical Subject Classification 2000
Primary: 16S99
Secondary: 16G20, 57N05, 57M50
Milestones
Received: 8 April 2009
Revised: 24 June 2009
Accepted: 6 August 2009
Published: 26 January 2010
Authors
Ibrahim Assem
Département de Mathématiques
Université de Sherbrooke
Sherbrooke, QC J1K 2R1
Canada
Thomas Brüstle
Département de Mathématiques
Université de Sherbrooke
Sherbrooke, QC J1K 2R1
Canada
Department of Mathematics
Bishop’s University
College St.
Sherbrooke, QC J1M 0C8
Canada
Gabrielle Charbonneau-Jodoin
Département de Mathématiques
Université de Sherbrooke
Sherbrooke, QC J1K 2R1
Canada
Pierre-Guy Plamondon
Institut de Mathématiques
Université Denis Diderot (Paris VII)
Case 7012-2, place Jussieu 75251 Paris Cedex 05
France