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)
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Official URL: https://doi.org/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, 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 |
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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 and Innovation Services |
Depositing User: | Bas Lemmens |
Date Deposited: | 28 Sep 2016 08:37 UTC |
Last Modified: | 09 Dec 2022 07:54 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/57539 (The current URI for this page, for reference purposes) |
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