Balanced Measures on Compact Median Algebras
Uri Bader, Aviv Taller

TL;DR
This paper explores the dynamics of group actions on compact median algebras, revealing that invariant measures are uniform on cubes and that amenable groups fix sub-cubes, advancing understanding of median algebra symmetries.
Contribution
It introduces a systematic approach to group actions on compact median algebras and characterizes invariant measures, connecting measure invariance to geometric structure.
Findings
Invariant measures are uniform on cubes.
Amenable group actions fix sub-cubes.
Provides a new framework for median algebra dynamics.
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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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Algebraic structures and combinatorial models
