Cyclic orders defined by ordered jordan algebras
arXiv:1706.09155
Abstract
We define a general notion of partially ordered Jordan algebra (over a partially ordered ring), and we show that the Jordan geometry associated to such a Jordan algebra admits a natural invariant partial cyclic order, whose intervals are modelled on the symmetric cone of the Jordan algebra. We define and describe, by affine images of intervals, the interval topology on the Jordan geometry, and we outline a reserch program aiming at generalizing main features of the theory of classical symmetric cones and bounded symmetric domains.
arXiv commentV2 : minor corrections and improvements. To appear in Journal of Lie Theory