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arXiv · 1302.4358

Non-direct limit of simple dimension groups with finitely many pure traces

David Handelman
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Abstract

There exist simple dimension groups which cannot be expressed as a direct limit of simple, or even approximately divisible dimension groups, each with finitely many pure traces, and we can specify its infinite-dimensional Choquet simplex of traces; a more drastic property is noted. On the other hand, a very easy argument shows that if $G$ is a $p$-divisible simple dimension group (for some integer $p>1$), then it can be expressed as such a direct limit. We also enlarge the class of initial objects for AF (and slightly more general) C*-algebras.

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David Handelman. 2013-02-18. Non-direct limit of simple dimension groups with finitely many pure traces. https://arxiv.org/abs/1302.4358

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