On the role of gentle algebras in Higher Homological algebra

Abstract: In higher homological algebra, (d+2)-angulated categories are higher analogues of triangulated categories. They primarily appear as d-cluster-tilting subcategories of triangulated categories closed under d-suspension. We give a complete classification of such d-cluster-tilting subcategories of the derived category of a gentle algebra by using the geometric model given by Opper-Plamondon-Schroll. It turns out that, up to derived equivalence, they occur only in Dynkin type A; in other words we have a puzzling lack of d-cluster-tilting subcategories associated to gentle algebras.

This is joint work with Johanne Haugland and Sibylle Schroll.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

( slides )

The TRAC Seminar - Théorie de Représentations et ses Applications et Connections