Ideals in Some Continuous Nonselfadjoint Crossed Product Algebras

Let (Y, φt) be a locally compact dynamical system, where theφtdenotes a continuous, one parameter semigroup of maps onY. When eachφtis a homeomorphism, a nonselfadjoint crossed product algebra is defined as the subalgebra of the C*-crossed productC0(Y)⋊R supported ont>0; when eachφtis only continuous, the crossed productC0(Y)⋊R+can still be defined. The ideal structure of such an algebra is determined in the case where the semigroup action is the suspension of a discrete, free action on a smaller spaceX. A generalization of Effros–Hahn is given, whereby one may find a meet-irreducible ideal over any arc closure inY. The meet-irreducible ideals form a topological space in the hull-kernel topology, and there is a one-to-one correspondence between closed sets in this space and closed ideals in the algebra. A subset of this space is homeomorphic to the space of finite arcs in the subarc topology. The irrational flow algebra is considered as a special case.