<i>C</i>*-Algebras Associated with Mauldin–Williams Graphs
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Abstract
Abstract A Mauldin–Williams graph is a generalization of an iterated function system by a directed graph. Its invariant set K plays the role of the self-similar set. We associate a C* -algebra ( K ) with a Mauldin–Williams graph and the invariant set K , laying emphasis on the singular points. We assume that the underlying graph G has no sinks and no sources. If satisfies the open set condition in K , and G is irreducible and is not a cyclic permutation, then the associated C* -algebra ( K ) is simple and purely infinite. We calculate the K -groups for some examples including the inflation rule of the Penrose tilings.
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