A categorification of non-crossing partitions

Hubery A, Krause H. A categorification of non-crossing partitions. Journal of the European Mathematical Socitey. 2016;18(10):2273-2313.We present a categorification of the non-crossing partitions given by crystallographic Coxeter groups. This involves a category of certain bilinear lattices, which are essentially determined by a symmetrisable generalised Cartan matrix together with a particular choice of a Coxeter element. Examples arise from Grothendieck groups of hereditary artin algebras