The ideal structure of some analytic crossed products

We study the ideal structure of a class of some analytic crossed products. For an r-discrete, principal, minimal groupoid G, we consider the analytic crossed product C*(G, sigma) x(alpha) Z(+), where alpha is given by a cocyc le c. We show that the maximal ideal space M of C*(G, sigma) x(alpha) Z(+) depends on the asymptotic range of c, R-infinity (c); that is, M is homeomo rphic to (D) over bar \ R-infinity (c) for R-infinity (c) finite, and M con sists of the unique maximal ideal for R-infinity (c) = T. We also prove tha t C*(G, sigma) x(alpha) Z(+) is semisimple in both cases, and that R-infini ty (c) is invariant under isometric isomorphism.