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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) (KAR id:57539)

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, that is, \(g (\lambda x) = \lambda^{-1}g(x)\) for all \(\lambda > 0\) and \( x \in C°\), and \(g\) is an order-antimorphism, that is, \(x ≤ c\space y\) 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 \(dim V ≥ 3\), 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: 19 Feb 2020 10:34 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/57539 (The current URI for this page, for reference purposes)
Lemmens, Bas: https://orcid.org/0000-0001-6713-7683
Roelands, Mark: https://orcid.org/0000-0002-8885-9156
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