Derived categories of skew-gentle algebras and orbifolds
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.
Keywords
Cite
@article{arxiv.2006.05836,
title = {Derived categories of skew-gentle algebras and orbifolds},
author = {Daniel Labardini-Fragoso and Sibylle Schroll and Yadira Valdivieso},
journal= {arXiv preprint arXiv:2006.05836},
year = {2021}
}
Comments
Version3: Minor corrections of typos and add references