Journal of the European Mathematical Society

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Volume 18, Issue 10, 2016, pp. 2273–2313
DOI: 10.4171/JEMS/641

Published online: 2016-09-19

A categorification of non-crossing partitions

Andrew Hubery[1] and Henning Krause[2]

(1) Universit├Ąt Bielefeld, Germany
(2) Universit├Ąt Bielefeld, Germany

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.

Keywords: Non-crossing partition, hereditary algebra, Grothendieck group, Weyl group, Coxeter group, exceptional sequence, symmetrisable generalised Cartan matrix, perpendicular category

Hubery Andrew, Krause Henning: A categorification of non-crossing partitions. J. Eur. Math. Soc. 18 (2016), 2273-2313. doi: 10.4171/JEMS/641