Topological boundaries of covariant representations

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 20 Feb 2023Embargo end date: 01 Jan 2021Publisher:Det Kgl. Bibliotek/Royal Danish LibraryJournal:MATHEMATICA SCANDINAVICA, volume 129 (issn: 0025-5521, eissn: 1903-1807,

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Authors: Amini, Massoud; Zavar, Sajad;

doi: 10.7146/math.scand.a-135771 , 10.48550/arxiv.2112.09491

arXiv: 2112.09491

Topological boundaries of covariant representations

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Abstract

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.

Keywords

46M10, 37C85, Mathematics - Operator Algebras, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Operator Algebras (math.OA)

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