Minimal dynamical systems on prime C*-algebras

We give a number of examples of exotic actions of locally compact groups on separable nuclear C*-algebras. In particular, we give examples of the following: (1) Minimal effective actions of $\mathbb{Z}$ and $F_n$ on unital nonsimple prime AF algebras. (2) For any second countable noncompact locally compact group, a minimal effective action on a separable nuclear nonsimple prime C*-algebra. (3) For any amenable second countable noncompact locally compact group, a minimal effective action on a separable nuclear nonsimple prime C*-algebra (unital when the group is $\mathbb{Z}$ or $\mathbb{R}$) such that the crossed product is $K\otimes {\mathcal{O}}_2$ (${\mathcal{O}}_2$ when the group is $\mathbb{Z}$). (4) For any second countable locally compact abelian group which is not discrete, an action on $K\otimes {\mathcal{O}}_2$ such that the crossed product is a nonsimple prime C*-algebra. In most of these situations, we can specify the primitive ideal space of the C*-algebra (of the crossed product in the last item) within a class of spaces.