Geodesic
Derived categories of skew-gentle algebras and orbifolds
Glasgow mathematical journal, Tome 64 (2022) no. 3, pp. 649-674

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DOI

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 Gröbner basis theory, we show that these algebras are strong 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 surfaces with orbifold points, 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. 
Labardini-Fragoso, Daniel; Schroll, Sibylle; Valdivieso, Yadira. Derived categories of skew-gentle algebras and orbifolds. Glasgow mathematical journal, Tome 64 (2022) no. 3, pp. 649-674. doi: 10.1017/S0017089521000422
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     author = {Labardini-Fragoso, Daniel and Schroll, Sibylle and Valdivieso, Yadira},
     title = {Derived categories of skew-gentle algebras and orbifolds},
     journal = {Glasgow mathematical journal},
     pages = {649--674},
     year = {2022},
     volume = {64},
     number = {3},
     doi = {10.1017/S0017089521000422},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089521000422/}
}
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