Balanced measures on compact median algebras

Uri Bader; Aviv Taller

doi:https://doi.org/10.1007/s10711-023-00778-y

Balanced measures on compact median algebras

Uri Bader, Aviv Taller

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We initiate a systematic investigation of group actions on compact median 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 fixes a sub-cube.

Original language	English
Article number	43
Journal	Geometriae Dedicata
Volume	217
Issue number	3
DOIs	https://doi.org/10.1007/s10711-023-00778-y
State	Published - 22 Feb 2023

Keywords

Amenable group
Median algebra
Probability measure

All Science Journal Classification (ASJC) codes

Geometry and Topology

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https://doi.org/10.1007/s10711-023-00778-y

http://arxiv.org/abs/2101.00437License: Unspecified

Cite this

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abstract = "We initiate a systematic investigation of group actions on compact median 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 fixes a sub-cube.",

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AB - We initiate a systematic investigation of group actions on compact median 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 fixes a sub-cube.

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KW - Probability measure

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Balanced measures on compact median algebras

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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