On wedges in Lie triple systems and ordered symmetric spaces
type: Item
instance of: scholarly article
title: On wedges in Lie triple systems and ordered symmetric spaces
zbMATH Open document ID: 0781.53040
DOI: 10.1007/BF01264091
author: Norbert Dörr
author: Karl-Hermann Neeb
published in: Geometriae Dedicata
publication date: 1994-02-17T00:00:00Z
review text: The authors develop an infinitesimal approach to the study of an order in an affine symmetric space \(M = G/H\) which is defined by an invariant field of convex cones \[ P: x\mapsto P_ x \in T_ xM. \] They associate with an ordered symmetric space \((M,P)\) a pair \((q,C)\), where \(q\) is a Lie triple system and \(C\) is a wedge in \(q\) which satisfies some conditions. Some relations between properties of an ordered symmetric space and the corresponding wedge are established. In particular, conditions that an ordered symmetric space \(M\) is globally hyperbolic are stated. An ordered manifold \(M\) is called globally hyperbolic if for any points \(x,y \in M\) the set \(\{z,x \leq z \leq y\}\) is compact.
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 17B99
zbMATH DE Number: 205520
zbMATH Keywords: order
zbMATH Keywords: symmetric space
zbMATH Keywords: convex cones
zbMATH Keywords: Lie triple system
zbMATH Keywords: globally hyperbolic
reviewed by: Dmitri Alekseevsky
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01264091
OpenAlex ID: W2053275083
description: scientific article; zbMATH DE number 205520