On the two-sided Guionnet-Jones-Shlyakhtenko construction at level three
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916982489612288 |
|---|---|
| author | Jayakumar, R |
| author_facet | Jayakumar, R |
| contents | We study the two-sided Guionnet-Jones-Shlyakhtenko construction applied to the group planar algebra $P(\mathcal{G})$ of a finite non-trivial group $\mathcal{G}$. This produces a sequence of von Neumann algebras $M^k$ for $k \geq 0$ with no natural inclusions. Focusing on level $k=3$, we show that the resulting von Neumann algebra $M^3$ is isomorphic to the interpolated free group factor LF$\left({1+\frac{2(n-1)}{n^2}}\right)$, where $n=|\mathcal{G}|$. Our approach keeps the combinatorics explicit and relies on standard tools from free probability and planar algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00747 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the two-sided Guionnet-Jones-Shlyakhtenko construction at level three Jayakumar, R Operator Algebras 46L37, 46L54 We study the two-sided Guionnet-Jones-Shlyakhtenko construction applied to the group planar algebra $P(\mathcal{G})$ of a finite non-trivial group $\mathcal{G}$. This produces a sequence of von Neumann algebras $M^k$ for $k \geq 0$ with no natural inclusions. Focusing on level $k=3$, we show that the resulting von Neumann algebra $M^3$ is isomorphic to the interpolated free group factor LF$\left({1+\frac{2(n-1)}{n^2}}\right)$, where $n=|\mathcal{G}|$. Our approach keeps the combinatorics explicit and relies on standard tools from free probability and planar algebras. |
| title | On the two-sided Guionnet-Jones-Shlyakhtenko construction at level three |
| topic | Operator Algebras 46L37, 46L54 |
| url | https://arxiv.org/abs/2510.00747 |