The $K$-Group of Substitutional Systems

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 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.