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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.20061 |
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| _version_ | 1866915647671238656 |
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| author | Dutkay, Dorin Ervin Georgescu, Catalin Picioroaga, Gabriel |
| author_facet | Dutkay, Dorin Ervin Georgescu, Catalin Picioroaga, Gabriel |
| contents | We provide a new characterization of amenability for countable groups, based on frame representations admitting almost invariant vectors. By relaxing the frame inequalities, thereby weakening amenability, we obtain a large class of countable groups which we call {\it framenable}. We show that this class has some permanence properties, stands in contrast with property (T), and contains, for example, all free groups $\mathbb{F}_n$, $\textup{Aut}(\mathbb{F}_2)$ and $\textup{Aut}(\mathbb{F}_3)$, all (countable) lattices of $SL(2,\mathbb{R})$, the Baumslag-Solitar groups $BS_{p,q}$, the braid groups $B_n$, and Thompson's group $F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frame Vector Group Representations and Amenability Properties Dutkay, Dorin Ervin Georgescu, Catalin Picioroaga, Gabriel Group Theory Functional Analysis 20F65, 22D10, 42C15, 46C05 We provide a new characterization of amenability for countable groups, based on frame representations admitting almost invariant vectors. By relaxing the frame inequalities, thereby weakening amenability, we obtain a large class of countable groups which we call {\it framenable}. We show that this class has some permanence properties, stands in contrast with property (T), and contains, for example, all free groups $\mathbb{F}_n$, $\textup{Aut}(\mathbb{F}_2)$ and $\textup{Aut}(\mathbb{F}_3)$, all (countable) lattices of $SL(2,\mathbb{R})$, the Baumslag-Solitar groups $BS_{p,q}$, the braid groups $B_n$, and Thompson's group $F$. |
| title | Frame Vector Group Representations and Amenability Properties |
| topic | Group Theory Functional Analysis 20F65, 22D10, 42C15, 46C05 |
| url | https://arxiv.org/abs/2508.20061 |