2025/02/18 by Sira Busch, Busch, Sira · 1 citation
Business, Management and Accounting · Engineering · Mathematics · #20E42 #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #Optics and Image Analysis #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2502.12857
openalex publication_date 2025/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give direct, geometric constructions for nontrivial root elations for rank 2 residues of higher rank buildings Δ of type Bn, Cn and Hm for n ∈ ℕ and m ∈ \3,4\. We show that we can extend these to the ambient building in the case that Δ has type Bn or Cn. With that, we obtain a different proof for the fact that buildings of type Bn and Cn are Moufang. This geometric approach enables us to gain more insight into the root groups associated to these buildings and we obtain new results; Namely, that certain root elations generically fix more points than we previously knew and that every root elation in each point residual can be written as an even self-projectivity. Concerning Hm, we will be able to see in a novel way why thick, spherical buildings of type Hm cannot exist. Altogther, this provides an alternative proof for the fact that all thick, irreducible, spherical buildings Δ of rank 3 have the Moufang property.