An order theoretic characterization of spin factors
| Autor: | Mark Roelands, Hent van Imhoff, Bas Lemmens |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
General Mathematics
010102 general mathematics Mathematics - Operator Algebras Order (ring theory) 0102 computer and information sciences 17C65 46B40 Characterization (mathematics) Lambda Space (mathematics) 01 natural sciences Functional Analysis (math.FA) Combinatorics Mathematics - Functional Analysis Cone (topology) 010201 computation theory & mathematics FOS: Mathematics Bijection QA299 0101 mathematics Operator Algebras (math.OA) Convex function Unit (ring theory) Mathematics |
| Zdroj: | The Quarterly Journal of Mathematics, 68(3), 1001-1017. Oxford University Press (OUP) |
| ISSN: | 0033-5606 |
| Popis: | 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 $g\colon C^\circ\to C^\circ$ with the property that $g$ is antihomogeneous, i.e., $g(\lambda x) =\lambda^{-1}g(x)$ for all $\lambda>0$ and $x\in C^\circ$, and $g$ is an order-antimorphism, i.e., $x\leq_C y$ if and only if $g(y)\leq_C g(x)$. 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 $\dim V\geq 3$, then there exists a bijective antihomogeneous order-antimorphism $g\colon C^\circ\to C^\circ$ if and only if $(V,C,u)$ is a spin factor. Comment: 15 pages (minor revisions). To appear in Quarterly Journal of Mathematics |
| Databáze: | OpenAIRE |
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