Property (T) group factors whose Jones index set equals all positive integers
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909894981976064 |
|---|---|
| author | Chifan, Ionut Lim, Junhwi |
| author_facet | Chifan, Ionut Lim, Junhwi |
| contents | Using a mélange of techniques at the rich intersection of deformation/rigidity theory, finite index subfactor theory, and geometric group theory, we prove the existence of a continuum of property (T) factors that are pairwise non-stably isomorphic and whose Jones index sets consist of all positive integers. These factors are realized as group von Neumann algebras $\mathcal{L}(G)$ associated with property (T) generalized wreath-like product groups $G \in \mathscr{WR}(A, B \curvearrowright I)$ introduced in [CIOS23b], where $A$ is abelian, $B$ is a non-parabolic subgroup of a relatively hyperbolic group with residually finite peripheral structure, and $B \curvearrowright I$ is a faithful action with infinite orbits. Integer index subfactors of $\mathcal{L}(G)$ are constructed from extensions of $G$. This result advances an open question of P. de la Harpe [dlH95]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04822 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Property (T) group factors whose Jones index set equals all positive integers Chifan, Ionut Lim, Junhwi Operator Algebras Group Theory Using a mélange of techniques at the rich intersection of deformation/rigidity theory, finite index subfactor theory, and geometric group theory, we prove the existence of a continuum of property (T) factors that are pairwise non-stably isomorphic and whose Jones index sets consist of all positive integers. These factors are realized as group von Neumann algebras $\mathcal{L}(G)$ associated with property (T) generalized wreath-like product groups $G \in \mathscr{WR}(A, B \curvearrowright I)$ introduced in [CIOS23b], where $A$ is abelian, $B$ is a non-parabolic subgroup of a relatively hyperbolic group with residually finite peripheral structure, and $B \curvearrowright I$ is a faithful action with infinite orbits. Integer index subfactors of $\mathcal{L}(G)$ are constructed from extensions of $G$. This result advances an open question of P. de la Harpe [dlH95]. |
| title | Property (T) group factors whose Jones index set equals all positive integers |
| topic | Operator Algebras Group Theory |
| url | https://arxiv.org/abs/2511.04822 |