We prove some injectivity results: that a Coxeter monoid \(\mathbb {Z}\)-algebra (or 0-Hecke algebra) injects in the incidence \(\mathbb {Z}\)-algebra of the corresponding Bruhat poset, for any Coxeter group; that the Hecke algebra of a right-angled Coxeter group injects in the Coxeter monoid \(\mathbb {Z}[q,q^{-1}]\)-algebra (and then in the incidence \(\mathbb {Z}[q,q^{-1}]\)-algebra of the corresponding Bruhat poset); that a right-angled Artin group injects in the group of invertible elements of the Hecke algebra of the corresponding Coxeter group (and then in the group of invertible elements of a Coxeter monoid algebra and in the one of an incidence algebra).

我们证明了一些内射性结果：Coxeter单面体\（\ mathbb {Z} \）-代数（或0-Hecke代数）注入对应的Bruhat球型的入射角\（\ mathbb {Z} \）-代数，任何Coxeter团体；直角Coxeter族的Hecke代数注入到Coxeter monoid \（\ mathbb {Z} [q，q ^ {-1}] \）-代数（然后是入射数\（\ mathbb {Z} [q，q ^ {-1}] \）-相应的Bruhat姿态的代数）；直角Artin组向相应Coxeter组的Hecke代数的可逆元素组注入（然后向Coxeter单对分代数的可逆元素组和入射代数之一）注入。