A categorification of non-crossing partitions

Published 7 Oct 2013 in math.RT and math.CO | (1310.1907v2)

Abstract: 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.

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