Actions of certain torsion-free elementary amenable groups on strongly self-absorbing C*-algebras

摘要

In this paper we consider a bootstrap class of countable discrete groups, which is closed under countable unions and extensions by the integers, and we study actions of such groups on algebras. This class includes all torsion-free abelian groups, poly-groups, as well as other examples. Using the interplay between relative Rokhlin dimension and semi-strongly self-absorbing actions established in prior work, we obtain the following two main results for any group Gamma is an element of C and any strongly self-absorbing There is a unique strongly outer up to (very strong) cocycle conjugacy. If alpha:Gamma is a strongly outer action on a separable, unital, nuclear, simple, -algebra with at most one trace, then it absorbs every Gamma action on up to (very strong) cocycle conjugacy. In fact we establish more general relative versions of these two results for actions of amenable groups that have a predetermined quotient in the class. For the monotracial case, the proof comprises an application of Matui-Sato's equivariant property (SI) as a key method.