Valuations on PTR's induced by triangle buildings
type: Item
instance of: scholarly article
title: Valuations on PTR's induced by triangle buildings
zbMATH Open document ID: 0639.51011
DOI: 10.1007/BF00148015
published in: Geometriae Dedicata
publication date: 1988-01-01T00:00:00Z
review text: Recently, \textit{J. Tits} [Lect. Notes Math. 1181, 159-190 (1986; Zbl 0611.20026)] classified all affine buildings of rank \(\geq 4\), they come from algebraic groups over a local field. There are affine buildings not arising in this way, the so-called non-classical ones. Their Buekenhout diagram is of three possible types. There are examples of non-classical buildings for each of the three possible types. The present paper describes the triangle buildings (i.e. buildings whose Buekenhout diagram is a triangle) as follows: There is a bijective correspondence between the class of triangle buildings (with a complete set of apartments) and the class of projective planes coordinatized by a complete planar ternary ring with valuation.
Mathematics Subject Classification ID: 51E25
zbMATH DE Number: 4042692
zbMATH Keywords: affine buildings
zbMATH Keywords: triangle buildings
zbMATH Keywords: Buekenhout diagram
zbMATH Keywords: planar ternary ring
author: Hendrik Van Maldeghem
reviewed by: László A. Székely
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00148015
OpenAlex ID: W2028988690
description: scientific article; zbMATH DE number 4042692