Matthew Pressland

Principal cluster categories.

Abstract:

I will describe constructions of 2-Calabi-Yau triangulated categories and stably 2-Calabi-Yau Frobenius categories. In particular, I will demonstrate how Amiot's 2-Calabi-Yau triangulated cluster category, usually defined via dg-algebras, may be realised as the stable category of the Frobenius category of Gorenstein projective modules over an ordinary algebra. One consequence of this approach is the construction of a categorification of the (polarised) principal coefficient cluster algebra associated to any acyclic quiver.