Group actions on topological graphs
Published online by Cambridge University Press: 16 September 2011
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)⋊rG 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 . We also define the fundamental group and the universal covering of a topological graph.
- Research Article
- Ergodic Theory and Dynamical Systems , Volume 32 , Issue 5: Daniel J. Rudolph – in Memoriam , October 2012 , pp. 1527 - 1566
- Copyright © Cambridge University Press 2011