Semisimplicial unital groups
type: Item
instance of: scholarly article
title: Semisimplicial unital groups
zbMATH Open document ID: 1076.81004
author: David J. Foulis
author: Richard J. Greechie
published in: International Journal of Theoretical Physics
publication date: 2005-03-15T00:00:00Z
review text: 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.
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 2146177
zbMATH Keywords: base-normed space
zbMATH Keywords: directed group
zbMATH Keywords: effect algebra
zbMATH Keywords: partially ordered abelian group
zbMATH Keywords: semisimplicial group
zbMATH Keywords: order-unit space
zbMATH Keywords: unital group
MaRDI profile type: Publication
DOI: 10.1023/B:IJTP.0000048814.76568.DE
description: scientific article; zbMATH DE number 2146177