2020/11/25 by Corina Ciobotaru, Ciobotaru, Corina
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Functional Analysis (math.FA) #Group Theory (math.GR) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2011.12921
openalex publication_date 2020/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Firstly, we prove that every closed subgroup H of type-preserving automorphisms of a locally finite thick affine building Δ of dimension ≥ 2 that acts strongly transitively on Δ is Moufang. If moreover Δ is irreducible and H is topologically simple, we show that H is the subgroup \G(k)+ of the k-rational points \G(k) of the isotropic simple algebraic group \G over a non-Archimedean local field k associated with Δ. Secondly, we generalise the proof given in \citeBM00b for the case of bi-regular trees to any locally finite thick affine building Δ, and obtain that any topologically simple, closed, strongly transitive and type-preserving subgroup of \Aut(Δ) has the Howe--Moore property. This proof is different than the strategy used so far in the literature and does not relay on the polar decomposition KA+K, where K is a maximal compact subgroup, and the important fact that A+ is an abelian maximal sub-semi-group.