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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29031 |
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Table of Contents:
- We investigate translation actions of countable dense subgroups of non-unimodular locally compact second countable (lcsc) groups. Using left-right actions, we show that the left translation action $Γ\curvearrowright G$ given by a countable dense subgroup $Γ$ of a locally compact second countable group $G$ can only be strongly ergodic if $G$ is almost unimodular. We show that the strong ergodicity of the action $Γ\curvearrowright G$ for an almost unimodular lcsc group $G$ is equivalent to the strong ergodicity of $Γ\cap \ker(Δ_G)\curvearrowright \ker(Δ_G)$, where $Δ_G$ is the modular function. We demonstrate the absence of rigidity, by showing that non-isomorphic lcsc almost unimodular groups can admit orbit equivalent translation actions.