REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: When working in higher homological algebra, one is dependent on finding d-cluster-tilting subcategories of abelian and triangulated categories. Using string combinatorics, we classify the d-cluster-tilting subcategories of the module category of a gentle algebra. We also classify the d-cluster-tilting subcategories of the derived category of a gentle algebra by using the geometric model given by Opper-Plamondon-Schroll. The result is a puzzling lack of d-cluster-tilting subcategories associated to gentle algebras. This is joint work with Johanne Haugland and Sibylle Schroll.