Group actions on topological graphs

الأصل · EN

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:E¹→ G. The group acts freely and properly on this new topological graph E×cG. If G is abelian, there is a dual action on C*(E) such that C*(E) G C*(E×cG). We also define the fundamental group and the universal covering of a topological graph.