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- W4300227777 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 ${mathcal H}(E)$ and on the graph $C^*$-algebra $C^*(E)$. If the action is free and proper, we prove that $C^*(E)rtimes_r G$ 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 $c:E^1to G$. The group acts freely and properly on this new topological graph $Etimes_cG$. If $G$ is abelian, there is a dual action on $C^*(E)$ such that $C^*(E)rtimes hat{G}cong C^*(Etimes_cG)$. We also define the fundamental group and the universal covering of a topological graph." @default.
- W4300227777 created "2022-10-03" @default.
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- W4300227777 date "2010-07-15" @default.
- W4300227777 modified "2023-09-25" @default.
- W4300227777 title "Group actions on topological graphs" @default.
- W4300227777 doi "https://doi.org/10.48550/arxiv.1007.2616" @default.
- W4300227777 hasPublicationYear "2010" @default.
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