Coverings of Directed Graphs and Crossed Products of C*-algebras by Coactions of Homogeneous Spaces

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The graph C*-algebra of a directed graph E is the universal C*-algebra generated by a family of partial isometries satisfying relations which reflect the path structure of E. In the first part of this paper we consider coverings of directed graphs: morphisms p:F->E which are local isomorphisms. We show that the graph algebra C*(F) can be recovered from C*(E) as a crossed product by a coaction of a homogeneous space associated to the fundamental group π_1 (E). These crossed products provide a good model for a general theory of crossed products by homogeneous spaces. The second part of the paper is devoted to building a framework for studying crossed products by homogeneous spaces using Rieffel's theory of proper actions.
15 pages with no figures

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Operator Algebras, 46L55

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http://salesiana.dossiersoluciones.com/handle/123456789/63045

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0201033
 http://arxiv.org/abs/math/0201033

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arXiv