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Journal of Lie Theory 28 (2018), No. 3, 643--661
Copyright Heldermann Verlag 2018

Cyclic Orders Defined by Ordered Jordan Algebras

Wolfgang Bertram
Institut E. Cartan, Université de Lorraine, B. P. 70239, 54506 Vandoeuvre-les-Nancy, France

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 research program aiming at generalizing main features of the theory of classical symmetric cones and bounded symmetric domains.

Keywords: Partial cyclic order, partial order, symmetric cone, partially ordered ring, interval topology, partially ordered Jordan algebra, Jordan geometry.

MSC: 06F25, 15B48, 17C37, 32M15, 53C35, 51G05

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