Gluing two affine spaces
type: Item
instance of: scholarly article
title: Gluing two affine spaces
zbMATH Open document ID: 0852.51012
author: Antonio Pasini
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1996-12-05T00:00:00Z
full work available at URL: https://eudml.org/doc/118941
review text: The author presents a detailed study of the gluing of two affine spaces over a commutative field \(K\) following the general theory described by \textit{F. Buekenhout}, \textit{C. Huybrechts} and the author in Bull. Belg. Math. Soc. Simon Stevin 1, No. 3, 355-397 (1994; Zbl 0809.51012) where some of these results were first announced. The author proves that the canonical gluing of two copies of \(AG (n,K)\) is a quotient of a certain subgeometry of the building of type \(D_{n + 1}\) over \(K\). The author also shows that the canonical gluing of two copies of the point-line system of \(AG (n,q)\) is characterized by its automorphism groups, which is as large as possible. Furthermore, with the exception of two cases, this gluing is characterized by a flag-transitivity condition.
Mathematics Subject Classification ID: 51E24
zbMATH DE Number: 885627
zbMATH Keywords: diagram geometries
zbMATH Keywords: flat geometries
zbMATH Keywords: gluing two affine spaces
reviewed by: Jacqui Ramagge
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 885627