Singularity categories of gentle algebras
Copyright policy )Singularity categories of gentle algebras
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 $\ct$.
11 pages; minor changes, final version, to appear Bulletin of the LMS
- University of Edinburgh United Kingdom
Jacobian algebra, 18E30, 16G20, Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.), Mathematics - Rings and Algebras, math.RT, Derived categories, triangulated categories, stable module categories, Rings and Algebras (math.RA), singularity categories, FOS: Mathematics, Representations of quivers and partially ordered sets, Cohen-Macaulay modules in associative algebras, Representation Theory (math.RT), Gorenstein projective modules, triangulated orbit categories, unpunctured marked Riemann surfaces, math.RA, Singularities of surfaces or higher-dimensional varieties, Mathematics - Representation Theory, gentle algebras, cluster categories
Jacobian algebra, 18E30, 16G20, Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.), Mathematics - Rings and Algebras, math.RT, Derived categories, triangulated categories, stable module categories, Rings and Algebras (math.RA), singularity categories, FOS: Mathematics, Representations of quivers and partially ordered sets, Cohen-Macaulay modules in associative algebras, Representation Theory (math.RT), Gorenstein projective modules, triangulated orbit categories, unpunctured marked Riemann surfaces, math.RA, Singularities of surfaces or higher-dimensional varieties, Mathematics - Representation Theory, gentle algebras, cluster categories
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