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arXiv · 0903.3347

Gentle algebras arising from surface triangulations

Ibrahim Assem·Thomas Brüstle·Gabrielle Charbonneau-Jodoin·Pierre-Guy Plamondon
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Abstract

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

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BibTeXRIS

Ibrahim Assem, Thomas Brüstle, Gabrielle Charbonneau-Jodoin, Pierre-Guy Plamondon. 2009-07-01. Gentle algebras arising from surface triangulations. https://arxiv.org/abs/0903.3347

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