Partial dynamical systems and AF C*-algebras

2003/01/28 by Justin R. Peters, Peters, Justin R., Ryan J. Zerr +1
Mathematics · #37A55 #46L80 #47L40 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:37A55 #msc:46L80 #msc:47L40

paper · pdf · doi:10.48550/arxiv.math/0301337

submitted to the Houston Journal of Mathematics

arxiv created 2003/01/28 · arxiv updated 2009/11/30

Abstract

We obtain a characterization in terms of dynamical systems of those r-discrete groupoids for which the groupoid C*-algebra is approximately finite-dimensional (AF). These ideas are then used to compute the K-theory for AF algebras by utilizing the actions of these partial homeomorphisms, and these K-theoretic calculations are applied to some specific examples of AF algebras. Finally, we show that, for a certain class of dimension groups, a groupoid can be obtained directly from the dimension group's structure whose associated C*-algebra has K₀ group isomorphic to the original dimension group.

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