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The K-group of substitutional systems

A. El Kacimi·R. Parthasarathy
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Abstract

In another article we associated a dynamical system to a non-properly ordered Bratteli diagram. In this article we describe how to compute the $K-$group $K_0$ of the dynamical system in terms of the Bratteli diagram. In the case of properly ordered Bratteli diagrams this description coincides with what is already known, namely the so-called dimension group of the Bratteli diagram. The new ordered group defined here is more relevant for non-properly ordered Bratteli diagrams. We use our main result to describe $K_0$ of a substitutional system.

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A. El Kacimi, R. Parthasarathy. 2006-02-01. The K-group of substitutional systems. https://arxiv.org/abs/math/0506305

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