Boundary maps and covariant representations

Mehrdad Kalantar; Eduardo Scarparo

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arXiv · 2106.06382

Boundary maps and covariant representations

Mehrdad Kalantar·Eduardo Scarparo

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Abstract

We extend applications of Furstenberg boundary theory to the study of $C^*$-algebras associated to minimal actions $\Gamma\!\curvearrowright\! X$ of discrete groups $\Gamma$ on locally compact spaces $X$. We introduce boundary maps on $(\Gamma,X)$-$C^*$-algebras and investigate their applications in this context. Among other results, we completely determine when $C^*$-algebras generated by covariant representations arising from stabilizer subgroups are simple. We also characterize the intersection property of locally compact $\Gamma$-spaces and simplicity of their associated crossed products.

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Mehrdad Kalantar, Eduardo Scarparo. 2021-06-11. Boundary maps and covariant representations. https://arxiv.org/abs/2106.06382

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