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)

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
DOI/Identification number:	10.1093/qmath/hax010
Subjects:	Q Science Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Divisions:	Central Services > Information Services Central Services > Universities at Medway Central Services > Research Services
Depositing User:	Bas Lemmens
Date Deposited:	28 Sep 2016 08:37 UTC
Last Modified:	29 May 2019 17:54 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/57539 (The current URI for this page, for reference purposes)