# An order theoretic characterization of spin factors

Lemmens, Bas, Roelands, Mark, Van Imhoff, Hent (2017) An order theoretic characterization of spin factors. The Quarterly Journal of Mathematics, 68 (3). pp. 1001-1017. ISSN 0033-5606. (doi:10.1093/qmath/hax010)

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## Abstract

The famous Koecher-Vinberg theorem characterizes the Euclidean Jordan algebras among the finite dimensional order unit spaces as the ones that have a symmetric cone. Recently Walsh gave an alternative characterization of the Euclidean Jordan algebras. He showed that the Euclidean Jordan algebras correspond to the finite dimensional order unit spaces (V,C,u) for which there exists a bijective map g:C?C with the property that g is antihomogeneous, i.e., g(?x)=(1/?)g(x) for all ?>0 and x?C, and g is an order-antimorphism, i.e., x?y if and only if g(y)?g(x). In this paper we make a first step towards extending this order theoretic characterization to infinite dimensional JB-algebras. We show that if (V,C,u) is a complete order unit space with a strictly convex cone and dimV?3, then there exists a bijective antihomogeneous order-antimorphism g:C?C if and only if (V,C,u) is a spin factor.

Item Type: Article 10.1093/qmath/hax010 Q ScienceQ Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Central Services > Information ServicesCentral Services > Universities at MedwayCentral Services > Research Services Bas Lemmens 28 Sep 2016 08:37 UTC 29 May 2019 17:54 UTC https://kar.kent.ac.uk/id/eprint/57539 (The current URI for this page, for reference purposes)