Scale and tidy subgroups for Weyl-transitive automorphism groups of buildings

Autor:	Baumgartner, Udo, Parkinson, James, Ramagge, Jacqui
Rok vydání:	2017
Předmět:	Mathematics - Group Theory 22D05 52E24 20E36 20F65
Druh dokumentu:	Working Paper
Popis:	We consider closed, Weyl-transitive groups of automorphisms of thick buildings. For each element of such a group, we derive a combinatorial formula for its scale and establish the existence of a tidy subgroup for it that equals the stabilizer of a simplex. Simplices whose stabilizers are tidy for some element of the group are characterized in terms of the minimal set of the isometry induced by the element on the Davis-realisation of the building and in terms of the Weyl-distance between them and their image. We use our results to derive some topological properties of closed, Weyl-transitive groups of automorphisms. Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1710.07881 Zobrazit plný text záznamu View this record from Arxiv