Cohomology of coloured partition algebras

Abstract

Coloured partition algebras were introduced by Bloss and exhibit a Schur-Weyl duality with certain complex reflection groups. In this paper we show that these algebras exhibit homological stability by demonstrating that their homology groups are stably isomorphic to the homology groups of a wreath product, generalizing work of Boyd--Hepworth--Patzt and Boyde for the usual partition algebras.

14 pages. Range of isomorphisms in main theorem extended by 1. Accepted for publication in Homology, Homotopy and Applications