Topological boundaries of covariant representations
DOI:
https://doi.org/10.7146/math.scand.a-135771Abstract
We associate a boundary $\mathcal B_{\pi ,u}$ to each covariant representation $(\pi ,u,H)$ of a $C^*$-dynamical system $(G,A,\alpha )$ and study the action of $G$ on $\mathcal B_{\pi ,u}$ and its amenability properties. We relate rigidity properties of traces on the associated crossed product $C^*$-algebra to faithfulness of the action of the group on this boundary.
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