2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161899We study different problems related to the Solomon's descent algebra $Σ(W)$ of a finite Coxeter group $(W,S)$: positive elements, morphisms between descent algebras, Loewy length... One of the main result is that, if $W$ is irreducible and if the longest element is central, then the Loewy length of $Σ(W)$ is equal to $\lceil |S| / 2 \rceil$.21 pagesRepresentation Theory20F55 (Primary); 05E99 (Secondary)text