Operator Algebras and Mauldin Williams Graphs

Details Operator Algebras and Mauldin Williams Graphs Operator Algebras and Mauldin Williams Graphs

2004-01-29

arxiv.org/abs/math/0401408v4

Mathematics

Operator Algebras

14 pages, Latex; Rewrote parts of the introduction and the proof of the first main theorem

Scientific paper

We describe a method for associating a $C^{*}$-correspondence to a Mauldin-Williams graph and show that the Cuntz-Pimsner algebra of this $C^{*}$-correspondence is isomorphic to the $C^{*}$-algebra of the underlying graph. In addition, we analyze certain ideals of these $C^{*}$-algebras. We also investigate Mauldin-Williams graphs and fractal $C^{*}$-algebras in the context of the Rieffel metric. This generalizes the work of Pinzari, Watatani and Yonetani. Our main result here is a {}``no go'' theorem showing that such algebras must come from the commutative setting.

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