# Boundary maps, germs and quasi-regular representations

@article{Kalantar2022BoundaryMG, title={Boundary maps, germs and quasi-regular representations}, author={Mehrdad Kalantar and Eduardo Scarparo}, journal={Advances in Mathematics}, year={2022} }

We investigate the tracial and ideal structures of $C^*$-algebras of quasi-regular representations of stabilizers of boundary actions. Our main tool is the notion of boundary maps, namely $\Gamma$-equivariant unital completely positive maps from $\Gamma$-$C^*$-algebras to $C(\partial_F\Gamma)$, where $\partial_F\Gamma$ denotes the Furstenberg boundary of a group $\Gamma$. For a unitary representation $\pi$ coming from the groupoid of germs of a boundary action, we show that there is a unique…

## 4 Citations

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We establish new results on the weak containment of quasi-regular and Koopman representations of a second countable locally compact group G associated with non-singular G-spaces. We deduce that any…

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We investigate the notion of relatively amenable topological action and show that the action of Thompson’s group T on
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