Group actions on topological graphs

Valentin Deaconu, Alex Kumjian, John Quigg

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We define the action of a locally compact group G on a topological graph E. This action induces a natural action of G on the C *- correspondence H(E) and on the graph C *-algebra C *(E). If the action is free and proper, we prove that C *(E)×r G is strongly Morita equivalent to C *(E/G). We define the skew product of a locally compact group G by a topological graph E via a cocycle c:E 1 → G. The group acts freely and properly on this new topological graph EA - c G. If G is abelian, there is a dual action on C * (E) such that $C*(E) {G}\cong C*(E×cG)$. We also define the fundamental group and the universal covering of a topological graph.

Original languageEnglish (US)
Pages (from-to)1527-1566
Number of pages40
JournalErgodic Theory and Dynamical Systems
Volume32
Issue number5
DOIs
StatePublished - Oct 1 2012

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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