Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.19481 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916966651920384 |
|---|---|
| author | Mejia, Juan Felipe Ariza Amaraweera, Dulanji Nikethani Chifan, Ionut Khan, Krishnendu |
| author_facet | Mejia, Juan Felipe Ariza Amaraweera, Dulanji Nikethani Chifan, Ionut Khan, Krishnendu |
| contents | In this paper we prove that whenever $G$ is hyperbolic relative to a family of exact, ressidually finite subgroups $\{H_1, \ldots, H_n\}$, the corresponding von Neumann algebra $\mathcal L(G)$ is solid relative to the family of subalgebras $\{\mathcal L(H_1),\ldots ,\mathcal L(H_n)\}$. Building on this result and combining it with findings from geometric group theory, we construct a continuum of icc property (T) relative hyperbolic groups that give rise to pairwise non virtually isomorphic factors, each of which has trivial one-sided fundamental semigroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19481 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative solidity results and their applications to computations of some II$_1$ factor invariants Mejia, Juan Felipe Ariza Amaraweera, Dulanji Nikethani Chifan, Ionut Khan, Krishnendu Operator Algebras In this paper we prove that whenever $G$ is hyperbolic relative to a family of exact, ressidually finite subgroups $\{H_1, \ldots, H_n\}$, the corresponding von Neumann algebra $\mathcal L(G)$ is solid relative to the family of subalgebras $\{\mathcal L(H_1),\ldots ,\mathcal L(H_n)\}$. Building on this result and combining it with findings from geometric group theory, we construct a continuum of icc property (T) relative hyperbolic groups that give rise to pairwise non virtually isomorphic factors, each of which has trivial one-sided fundamental semigroup. |
| title | Relative solidity results and their applications to computations of some II$_1$ factor invariants |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2509.19481 |