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arXiv · 2006.05836

Derived categories of skew-gentle algebras and orbifolds

Daniel Labardini-Fragoso·Sibylle Schroll·Yadira Valdivieso
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Abstract

Skew-gentle algebras are a generalisation of the well-known class of gentle algebras with which they share many common properties. In this work, using non-commutative Gr\"obner basis theory, we show that these algebras are Koszul and that the Koszul dual is again skew-gentle. We give a geometric model of their bounded derived categories in terms of polygonal dissections of orbifold surfaces establishing a correspondence between curves in the orbifold and indecomposable objects. Moreover, we show that the orbifold dissections encode homological properties of skew-gentle algebras such as their singularity categories, their Gorenstein dimensions and derived invariants such as the determinant of their q-Cartan matrices.

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Daniel Labardini-Fragoso, Sibylle Schroll, Yadira Valdivieso. 2020-06-10. Derived categories of skew-gentle algebras and orbifolds. https://arxiv.org/abs/2006.05836

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