Semisimplicial unital groups
The authors are interested study of finite effect algebras that arise as intervals in partially ordered abelian groups. They concentrate on semisimple unital groups, which are torsion free and have a finite unit interval. For such a group \(G\), the aditive group homomorphisms \(G \to\mathbb R\) form a directed partially ordered linear space over \(\mathbb R\), which actually is a base normed Banach space [\textit{T. A. Cook} and \textit{D. J. Foulis}, The base-normed space of a unital group. Math. Slovaca 54, No. 1, 69--85 (2004)]. In the paper under review, \(V(G)\) is represented as the Banach dual space of an finite dimensional order-unit space which contains \(G\) as an additive subgroup. Then a new necessary and sufficient condition for \(G\) to be archimedian, formulated in terms of this representation, is given.
scientific article; zbMATH DE number 2146177