Balanced Measures on Compact Median Algebras

2021/01/02 by Uri Bader, Bader, Uri, Aviv Taller +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.2101.00437

openalex publication_date 2021/01/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We initiate a systematic investigation of group actions on compact medain algebras via the corresponding dynamics on their spaces of measures. We show that a probability measure which is invariant under a natural push forward operation must be a uniform measure on a cube and use this to show that every amenable group action on a locally convex compact median algebra fixed a sub-cube.

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