Geodesic
Generalized Descent Algebras
Canadian mathematical bulletin, Tome 50 (2007) no. 4, pp. 535-546

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DOI

If $A$ is a subset of the set of reflections of a finite Coxeter group $W$ , we define a sub- $\mathbb{Z}$ -module ${{\mathcal{D}}_{A}}\left( W \right)$ of the group algebra $\mathbb{Z}W$ . We discuss cases where this submodule is a subalgebra. This family of subalgebras includes strictly the Solomon descent algebra, the group algebra and, if $W$ is of type $B$ , the Mantaci–Reutenauer algebra.
DOI : 10.4153/CMB-2007-052-4
Mots-clés : 20F55, 05E15, Coxeter group, Solomon descent algebra, descent set 
Hohlweg, Christophe. Generalized Descent Algebras. Canadian mathematical bulletin, Tome 50 (2007) no. 4, pp. 535-546. doi: 10.4153/CMB-2007-052-4
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     author = {Hohlweg, Christophe},
     title = {Generalized {Descent} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {535--546},
     year = {2007},
     volume = {50},
     number = {4},
     doi = {10.4153/CMB-2007-052-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-052-4/}
}
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