Journal of Lie Theory

no. 3
Cyclic Orders Defined by Ordered Jordan Algebras
Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 643-661
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.
DOI: 10.5802/jolt.1018
Classification: 06F25, 15B48, 17C37, 32M15, 53C35, 51G05
Keywords: Partial cyclic order, partial order, symmetric cone, partially ordered ring, interval topology, partially ordered Jordan algebra, Jordan geometry 
@article{JOLT_2018_28_3_a2,
     author = {W. Bertram},
     title = {Cyclic {Orders} {Defined} by {Ordered} {Jordan} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {643--661},
     year = {2018},
     volume = {28},
     number = {3},
     doi = {10.5802/jolt.1018},
     zbl = {1499.06055},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1018/}
}
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%A W. Bertram
%T Cyclic Orders Defined by Ordered Jordan Algebras
%J Journal of Lie Theory
%D 2018
%P 643-661
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W. Bertram. Cyclic Orders Defined by Ordered Jordan Algebras. Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 643-661. doi: 10.5802/jolt.1018

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