Coactions and skew products for topological quivers

Abstract

Given a cocycle on a topological quiver by a locally compact group, the author constructs a skew product topological quiver and determines conditions under which a topological quiver can be identified as a skew product. We investigate the relationship between the ${C^*}$ -algebra of the skew product and a certain native coaction on the ${C^*}$ -algebra of the original quiver, finding that the crossed product by the coaction is isomorphic to the skew product. As an application, we show that the reduced crossed product by the dual action is Morita equivalent to the ${C^*}$ -algebra of the original quiver.