Abstract: Ideals in some continuous  nonselfadjoint crossed product algebras

To appear: Journal of Functional Analysis

Let $(Y,\phi_t)$ be a locally compact dynamical system, where the $\phi_t$
denotes a continuous, one parameter semigroup of maps on $Y$. When each $\phi_t$
is a homeomorphism, a nonselfadjoint crossed product algebra is defined as the
subalgebra of the C*-crossed product $C_0(Y) x R$ supported on  $t>0$; when
each $\phi_t$ is only continuous, the crossed product $C_0(Y) x R^+$ 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
space $X$. A generalization of Effros-Hahn is given, whereby one may find a
meet-irreducible ideal over any arc closure in  $Y$. 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.

Michael P. Lamoureux
University of Calgary