Gentle algebras arising from surface triangulations

Details Gentle algebras arising from surface triangulations Gentle algebras arising from surface triangulations

2009-03-19

arxiv.org/abs/0903.3347v2

Mathematics

Representation Theory

37 pages, with more examples and details than the first version

Scientific paper

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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