Operator Algebras and Mauldin Williams Graphs
算子代数
2007-05-23 v4
摘要
We describe a method for associating a -correspondence to a Mauldin-Williams graph and show that the Cuntz-Pimsner algebra of this -correspondence is isomorphic to the -algebra of the underlying graph. In addition, we analyze certain ideals of these -algebras. We also investigate Mauldin-Williams graphs and fractal -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.
引用
@article{arxiv.math/0401408,
title = {Operator Algebras and Mauldin Williams Graphs},
author = {Marius Ionescu},
journal= {arXiv preprint arXiv:math/0401408},
year = {2007}
}
备注
14 pages, Latex; Rewrote parts of the introduction and the proof of the first main theorem