The invariant random order extension property is equivalent to amenability
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910521763037184 |
|---|---|
| author | Alpeev, Andrei |
| author_facet | Alpeev, Andrei |
| contents | Recently, Glasner, Lin and Meyerovitch gave a first example of a partial invariant order on a certain group that cannot be invariantly extended to an invariant random total order. Using their result as a starting point we prove that any invariant random partial order on a countable group could be invariantly extended to an invariant random total order iff the group is amenable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_14177 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The invariant random order extension property is equivalent to amenability Alpeev, Andrei Dynamical Systems Group Theory Recently, Glasner, Lin and Meyerovitch gave a first example of a partial invariant order on a certain group that cannot be invariantly extended to an invariant random total order. Using their result as a starting point we prove that any invariant random partial order on a countable group could be invariantly extended to an invariant random total order iff the group is amenable. |
| title | The invariant random order extension property is equivalent to amenability |
| topic | Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2206.14177 |