The geometry of null systems, Jordan algebras and von Staudt's theorem.
type: Item
instance of: scholarly article
title: The geometry of null systems, Jordan algebras and von Staudt's theorem.
zbMATH Open document ID: 1038.17023
author: Wolfgang Bertram
publication date: 2003-03-17T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/116033
review text: The paper under review extends definitions and results on generalized projective and polar geometry and their equivalence with the Jordan structures of the author's recent paper [Adv. Geom. 2, 329--369 (2002; Zbl 1035.17043)]. The main topic of this work is that the generalization of a connected generalized projective geometry \((X, X')\) over a commutative ring \(K\) with unit \(1\) and \({1\over 2}\in K\), is given by spaces corresponding to unital Jordan algebras, that is Jordan pair together with a distinguished invertible element. Also, the geometric interpretation of unital Jordan algebras is discussed. Precisely, there is canonically associated to the geometry \((X, X')\) a class of symmetric spaces. Additionally, a generalization is given to the well-known von Staudt's theorem [\textit{M. Berger}, Geometry I, II. Berlin: Springer-Verlag (1987; Zbl 0606.51001), Reprint Springer (1994)].
reviewed by: Demetra Demetropoulou-Psomopoulou
Mathematics Subject Classification ID: 17C37
Mathematics Subject Classification ID: 51A05
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 1883518
zbMATH Keywords: null-system
zbMATH Keywords: projective geometry
zbMATH Keywords: polar geometry
zbMATH Keywords: symmetric space
zbMATH Keywords: Jordan algebra
MaRDI profile type: Publication
OpenAlex ID: W5796299
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DOI: 10.5802/AIF.1942
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1883518