A $\tau$-Tilting Approach to Dissections of Polygons

[摘要] We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support $\tau$-tilting simplicial complex of an explicit finite dimensional algebra. To this end, we prove a property of some induced subcomplexes of support $\tau$-tilting simplicial complexes of finite dimensional algebras.

[关键词] dissections of polygons;accordion complexes;τ -tilting theory;representations of finite dimensional algebras;g-vectors