2020/06/10 by Labardini-Fragoso, Daniel, Schroll, Sibylle, Valdivieso, Yadira
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2006.05836
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 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.