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arXiv · 1207.6941

Singularity categories of gentle algebras

Martin Kalck
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Abstract

We determine the singularity category of an arbitrary finite dimensional gentle algebra $Λ$. It is a finite product of $n$-cluster categories of type $\mathbb{A}_{1}$. Equivalently, it may be described as the stable module category of a selfinjective gentle algebra. If $Λ$ is a Jacobian algebra arising from a triangulation $\ct$ of an unpunctured marked Riemann surface, then the number of factors equals the number of inner triangles of $\ct$.

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Martin Kalck. 2014-10-21. Singularity categories of gentle algebras. https://doi.org/10.1112/blms%2Fbdu093

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