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Singularity categories of gentle algebras

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Original languageEnglish
Publication statusPublished - 30 Jul 2012


We determine the singularity category of an arbitrary finite dimensional gentle algebra $\Lambda$. 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 $\Lambda$ 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 $\ct$.

    Research areas

  • math.RT, math.RA, 18E30, 16G20

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