Locally compact group actions on C∗-algebras and compact subgroups

Discrete C*-coactions and C*-algebraic bundles

“…In the case of nuclearity, we get the best result for amenable G: if any one of the three algebras is nuclear, then all are. The results of this section are analogous to, and in some cases generalize, results concerning compact abelian group actions appearing in [11], [12], [16], and [18]. Also, there is a little overlap with results independently discovered by Ng [15].…”

Compact Actions Commuting with Ergodic Actions and Applications to Crossed Products

“…In this case A& and A Xß K are strongly Morita equivalent in the sense of Rieffel [12]. In [10] it is proved that the action ß is saturated if and only if Aß(n)*Aß(n) = A® B(Hn)a®adn for every n £ K .…”

“…In [10] we have obtained necessary and sufficient conditions in order that the crossed product A Xß K of A by a compact group action (K, ß), be simple or prime. Namely, we have proved, in particular, the following result:…”

“…We have shown in [10,Example 3.9] that the simplicity (resp. primeness) of A^ together with the condition (2)(b) does not necessarily imply the simplicity (resp.…”

“…Using our earlier results contained in [10] we obtain results concerning the simplicity and primeness of the cross product in terms of the ergodicity of the commutant of the (compact) action. We then indicate some open problems in this theory.…”