Nikolaus Conference 2023

Speaker: Philippe Nadeau (Lyon)

Title: Koszulity of the Algebra of the Dual Braid Monoid


For any Coxeter group \(W\) and Coxeter element \(c\), Bessis defined its "dual braid monoid" extending Birman--Ko--Lee's construction in type \(A\). We show that the algebra \(A(W,c)\) of this monoid has the Koszul property, explaining in particular a certain identity involving the Moebius function of the monoid and the positive part \(K^+(W,c)\) of the cluster complex of \((W,c)\). The multiplication in the dual Koszul algebra \(A^{\dagger}(W,c)\) can moreover be described geometrically in terms of \(K^+(W,c)\). This is joint work with Matthieu Josuat-Verg├Ęs.

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