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The Furstenberg Boundary of a Groupoid

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arxiv 1904.10062 v2 pith:SNCUZA77 submitted 2019-04-22 math.OA

Clemens Borys This is my paper · ORCID
classification math.OA
keywords boundarycompactfurstenberggroupoidcriterionenvelopeetalehausdorff
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We define the Furstenberg boundary of a locally compact Hausdorff \'etale groupoid, generalising the Furstenberg boundary for discrete groups, by providing a construction of a groupoid-equivariant injective envelope. Using this injective envelope, we establish the absence of recurrent amenable subgroups in the isotropy as a sufficient criterion for the intersection property of a locally compact Hausdorff \'etale groupoid with compact unit space and no fixed points. This yields a criterion for C*-simplicity of minimal groupoids.

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  1. Regular ideals, Ideal Intersections and Quotients II

    math.OA 2025-09 accept novelty 6.0 of 10

    Regular inclusions with a faithful invariant pseudo-expectation have their regular ideals determined by invariant regular ideals of the subalgebra, and quotients by regular ideals preserve the pseudo-Cartan property a...

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