Partial dynamical systems and AF C*-algebras

Details Partial dynamical systems and AF C*-algebras Partial dynamical systems and AF C*-algebras

2003-01-28

arxiv.org/abs/math/0301337v1

Mathematics

Operator Algebras

submitted to the Houston Journal of Mathematics

Scientific paper

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 K_0 group isomorphic to the original dimension group.

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