We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on C*-algebras.

We show that the Morita equivalence part of Mansfield's Imprimitivity Theory can be obtained by Green's Imprimitivity Theorem (and duality theory).

In this short article, we will give several results concerning closed invariant ideals of crossed products using some "topological arguments".

We will define two canonical cohomology theories for Hopf C -algebras and for Hopf von Neumann algebras (with coefficients in their comodules). We will then study the situations when these cohomologies vanish. The cases of locally compact groups and compact quantum groups will be considered in more details.

Suppose that (A, G, α) is a C -dynamical system such that G is of polynomial growth. If A is finite dimensional, we show that any element in K (G; A) has slow growth and that L1 (G,A) is *-regular. Furthermore, if G is discrete and π is a "nice representation" of A, we define a new Banach-algebra l1 (G,A) which coincides with l1 (G; A) when A is finite dimensional. We also show that any element in K (G; A) has slow growth and l1 (G,A) is-regular.