Galois involutions and exceptional buildings
type: Item
instance of: scholarly article
title: Galois involutions and exceptional buildings
zbMATH Open document ID: 1366.20018
DOI: 10.4171/LEM/62-1/2-13
author: Bernhard Mühlherr
author: Richard M. Weiss
published in: L'Enseignement Mathématique. 2e Série
publication date: 2017-03-13T00:00:00Z
review text: The theory of descent in buildings developed in [\textit{B. Mühlherr} et al., Descent in buildings. Princeton, NJ: Princeton University Press (2015; Zbl 1338.51002)] deals with the connections between a spherical building and its ambient split building. The authors now apply this theory to give elementary constructions of the exceptional buildings that arise as fixed-point buildings of Galois involutions. The first 9 sections provide background material. The later sections construct the Moufang quadrangles of type \(\mathrm{E}_8\), \(\mathrm{E}_7\), \(\mathrm{E}_6\), the exceptional buildings of type \(\mathrm{A}_2\) (Moufang planes obtained from octonion division algebras) and the non-pseudo-split buildings of type \(\mathrm{F}_4\) (obtained from certain composition algebras). The last two sections construct the Moufang quadrangles of type \(\mathrm{F}_4\), in a similar fashion as in [\textit{B. Mühlherr} and \textit{H. Van Maldeghem}, Can. J. Math. 51, No. 2, 347--371 (1999; Zbl 0942.51002)].
reviewed by: Theo Grundhöfer
Mathematics Subject Classification ID: 20E42
Mathematics Subject Classification ID: 51E24
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20G41
zbMATH DE Number: 6694058
zbMATH Keywords: building
zbMATH Keywords: descent
zbMATH Keywords: Moufang quadrangle
zbMATH Keywords: exceptional building
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/lem/62-1/2-13
OpenAlex ID: W2583062995
description: scientific article; zbMATH DE number 6694058