Operator Algebras and Mauldin-Williams Graphs

Operator Algebras and Mauldin Williams Graphs

We describe a method for associating a C-correspondence to a Mauldin-Williams graph and show that the Cuntz-Pimsner algebra of this Ccorrespondence 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...

O ct 2 00 4 OPERATOR ALGEBRAS AND MAULDIN - WILLIAMS GRAPHS

We describe a method for associating a C-correspondence to a Mauldin-Williams graph and show that the Cuntz-Pimsner algebra of this Ccorrespondence 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...

Mauldin-williams Graphs, Morita Equivalence and Isomorphisms

We describe a method for associating some non-self-adjoint algebras to MauldinWilliams graphs and we study the Morita equivalence and isomorphism of these algebras. We also investigate the relationship between the Morita equivalence and isomorphism class of the C∗-correspondences associated with Mauldin-Williams graphs and the dynamical properties of the Mauldin-Williams graphs.

Universal Operator Algebras of Directed Graphs

Given a directed graph, there exists a universal operator algebra and universal C∗-algebra associated to the directed graph. For finite graphs this algebra decomposes as the universal free product of some building block operator algebras. For countable directed graphs, the universal operator algebras arise as direct limits of operator algebras of finite subgraphs. Finally, a method for computin...

Operator Theory and Operator Algebras