Topological Quiver \(C^*\)-Algebras & Group Actions

Topological quivers are a somewhat natural generalization of topological graphs, where we insist that edge space is additionally endowed with a family of Radon measures, indexed by the vertex space, satisfying some regularity conditions. In this series of talks, we aim to present the needed background material to understand what a topological quiver \(C^*\)-algebra is, as well as discuss some results we hope to generalize from Deaconu, Kumjian and Quigg in the topological graph setting. One of these main results being that a locally compact group acting freely and properly on a topological quiver induces a Morita equivalence between the reduced crossed product of the quiver \(C^*\)-algebra and the \(C^*\)-algebra of the corresponding ‘quotient quiver’.