Admissible submonoids of Artin-Tits monoids

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dc.creatorCastella, Anatole
dc.date2008-04-04
dc.date.accessioned2026-07-07T12:18:06Z
dc.date.available2026-07-07T12:18:06Z
dc.descriptionWe show the analogue of Muhlherr's [Coxeter groups in Coxeter groups, Finite Geom. and Combinatorics, Cambridge Univ. Press (1993), 277-287] for Artin-Tits monoids, and for Artin-Tits groups of spherical type. That is, the submonoid (resp. subgroup) of an Artin-Tits monoid (resp. group of spherical type) induced by an admissible partition of the Coxeter graph is an Artin-Tits monoid (resp. group). This generalizes and unifies the situation of the submonoid (resp. subgroup) of fixed elements of an Artin-Tits monoid (resp. group of spherical type) under the action of graph automorphisms, and the notion of LCM-homomorphisms defined by Crisp in [Injective maps between Artin groups, Geom. Group Theory Down Under, Canberra (1996) 119-137] and generalized by Godelle in [Morphismes injectifs entre groupes d'Artin-Tits, Algebr. Geom. Topol. 2 (2002), 519--536]. We then complete the classification of the admissible partitions for which the Coxeter graphs involved have no infinite label, started by Muhlherr in [Some contributions to the theory of buildings based on the gate property, Dissertation, Tübingen (1994)]. This leads us to the classification of Crisp's LCM-homomorphisms.
dc.identifierhttps://arxiv.org/abs/0804.0704
dc.identifierhttp://arxiv.org/abs/0804.0704
dc.identifierJournal of Pure and Applied Algebra, 212 (2008) 1594-1611
dc.identifierdoi:10.1016/j.jpaa.2007.10.010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212297
dc.subjectGroup Theory
dc.subject20F36
dc.titleAdmissible submonoids of Artin-Tits monoids
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