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We define a general notion of partially ordered Jordan algebra (over apartially ordered ring), and we show that the Jordan geometry associated tosuch a Jordan algebra admits a natural invariant partial cyclic order, whoseintervals are modelled on the symmetric cone of the Jordan algebra. We defineand describe, by affine images of intervals, the interval topology on theJordan geometry, and we outline a reserch program aiming at generalizing mainfeatures of the theory of classical symmetric cones and bounded symmetricdomains.

Cyclic orders defined by ordered jordan algebras