CROSSED PRODUCTS OF UHF ALGEBRAS BY PRODUCT TYPE ACTIONS

We study the primitive ideal spectrum of the C*-crossed product of a UHF algebra by certain product type actions of locally compact abelian groups. Any second countable group can be represented in this way with Γ-spectrum equal to the dual group, i.e. such that the crossed product is primitive, but the crossed product is never simple if the group has a nontrivial connected group as a direct summand, it may or may not be simple if the group is totally disconnected non-discrete, and it is always simple if the group is discrete. © 1979 Duke University Press.