Partial Dynamical Systems and AF C*-algebras

• Autores: Ryan J. Zerr, Justin R. Peters
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 2, 2005, págs. 463-494
• Idioma: inglés
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• Resumen

  • 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 its dimension group isomorphic to the original dimension group.