On wedges in Lie triple systems and ordered symmetric spaces
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.
scientific article; zbMATH DE number 205520