Simple archimedean dimension groups

TL;DR

This paper constructs simple, archimedean dimension groups with prescribed metrizable Choquet simplexes as their trace spaces, answering a question posed by Goodearl.

Contribution

It provides a method to realize any metrizable Choquet simplex as the trace space of a simple, archimedean dimension group, expanding the understanding of their structure.

Findings

Constructed dimension groups for all metrizable Choquet simplexes.

Established the simplicity and archimedean properties of these groups.

Connected the trace space of the groups to the given Choquet simplex.

Abstract

We answer a question of Goodearl, by constructing for every metrizable Choquet simplex, a dimension group that is simple and archimedean and whose trace space is the desired Choquet simplex.