Measure equivalence embeddings of free groups and free group factors
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909584948461568 |
|---|---|
| author | Berendschot, Tey Vaes, Stefaan |
| author_facet | Berendschot, Tey Vaes, Stefaan |
| contents | We give a simple and explicit proof that the free group $\mathbb{F}_2$ admits a measure equivalence embedding into any nonamenable locally compact second countable (lcsc) group $G$. We use this to prove that every nonamenable lcsc group $G$ admits strongly ergodic actions of any possible Krieger type and admits nonamenable, weakly mixing actions with any prescribed flow of weights. We also introduce concepts of measure equivalence and measure equivalence embeddings for $II_1$ factors. We prove that a $II_1$ factor $M$ is nonamenable if and only if the free group factor $L(\mathbb{F}_2)$ admits a measure equivalence embedding into $M$. We prove stability of property (T) and the Haagerup property under measure equivalence of $II_1$ factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11704 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Measure equivalence embeddings of free groups and free group factors Berendschot, Tey Vaes, Stefaan Group Theory Dynamical Systems Operator Algebras We give a simple and explicit proof that the free group $\mathbb{F}_2$ admits a measure equivalence embedding into any nonamenable locally compact second countable (lcsc) group $G$. We use this to prove that every nonamenable lcsc group $G$ admits strongly ergodic actions of any possible Krieger type and admits nonamenable, weakly mixing actions with any prescribed flow of weights. We also introduce concepts of measure equivalence and measure equivalence embeddings for $II_1$ factors. We prove that a $II_1$ factor $M$ is nonamenable if and only if the free group factor $L(\mathbb{F}_2)$ admits a measure equivalence embedding into $M$. We prove stability of property (T) and the Haagerup property under measure equivalence of $II_1$ factors. |
| title | Measure equivalence embeddings of free groups and free group factors |
| topic | Group Theory Dynamical Systems Operator Algebras |
| url | https://arxiv.org/abs/2212.11704 |