Geodesic
Cyclic Orders Defined by Ordered Jordan Algebras
Wolfgang Bertram1
1Institut E. Cartan, Université de Lorraine, B. P. 70239, 54506 Vandoeuvre-les-Nancy, France
Journal of Lie Theory, Tome 28 (2018) no. 3, pp. 643-661

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 06F25, 15B48, 17C37, 32M15, 53C35, 51G05
Mots-clés : Partial cyclic order, partial order, symmetric cone, partially ordered ring, interval topology, partially ordered Jordan algebra, Jordan geometry

Wolfgang Bertram  1

1 Institut E. Cartan, Université de Lorraine, B. P. 70239, 54506 Vandoeuvre-les-Nancy, France 
Wolfgang Bertram. Cyclic Orders Defined by Ordered Jordan Algebras. Journal of Lie Theory, Tome 28 (2018) no. 3, pp. 643-661. http://geodesic.mathdoc.fr/item/JOLT_2018_28_3_a2/
@article{JOLT_2018_28_3_a2,
     author = {Wolfgang Bertram},
     title = {Cyclic {Orders} {Defined} by {Ordered} {Jordan} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {643--661},
     year = {2018},
     volume = {28},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2018_28_3_a2/}
}
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