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Bibliographic Metadata

  • Title
    A dynamical core for topological directed graphs
  • Author
    Brenken, Berndt
  • Is part of
    Münster Journal of Mathematics, Issue Münster Journal of Mathematics, page 111-144
  • Published
    2010
  • Language
    German
  • Document type
    Journal Article
  • URN
    urn:nbn:de:hbz:6-16409479501 
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  •  The document is publicly available on the WWW
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Abstract
  • A topological graph, or quiver, is a directed graph where the edge and vertex spaces are topological spaces. The C*-algebra associated with the graph is a Cuntz-Pimsner algebra of an associated C*-correspondence over an abelian C*-algebra. For a given graph satisfying a properness hypothesis we construct and abstractly characterize a subgraph containing the iterative dynamical core of the original graph. The C*-algebra of this subgraph is a quotient of the C*-algebra of the graph, and under some additional assumptions is a crossed product C*-algebra by a shift endomorphism. This is accomplished using a composition product of topological graphs.