$AF$ Embedding of Crossed Products of Certain Graph $C^*$-Algebras by Quasi-free Actions

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dc.creatorFang, Xiaochun
dc.date2005-10-26
dc.date.accessioned2026-07-07T06:47:54Z
dc.date.available2026-07-07T06:47:54Z
dc.descriptionWe introduce the labelling map and the quasi-free action of a locally compact abelian group on a graph $C^*$-algebra of a row-finite directed graph. Some necessary conditions for embedding the crossed product to an $AF$ algebra are discussed, and one sufficient condition is proved that if the row-finite directed graph is constructed by possibly attaching some 1-loops to a row-finite directed graph whose each weak connected component is a rooted (possibly infinite) directed tree, and the labelling map is almost proper, which is proved to be a reasonable generalization of the earlier case, then the crossed product can be embedded to an $AF$ algebra.
dc.identifierhttps://arxiv.org/abs/math/0510551
dc.identifierhttp://arxiv.org/abs/math/0510551
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103811
dc.subjectOperator Algebras
dc.subject46L05;19K33
dc.title$AF$ Embedding of Crossed Products of Certain Graph $C^*$-Algebras by Quasi-free Actions
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