Conjugate pairs of Hadamard subfactors and vertex models
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909789311729664 |
|---|---|
| author | Bakshi, Keshab Chandra Guin, Satyajit Guruprasad |
| author_facet | Bakshi, Keshab Chandra Guin, Satyajit Guruprasad |
| contents | We show that any two Hadamard subfactors arising from a pair of distinct complex Hadamard matrices of order 3 are either equal or conjugate by a unitary in the relative commutant of their intersection. Moreover, when the Hadamard subfactors are not equal, we prove the factoriality of their intersection, and it turns out to be a vertex model subfactor. We compute the first relative commutant and characterize this subfactor by identifying it with a particular type of Krishnan-Sunder subfactor. A few key invariants, including the Pimsner-Popa probabilistic number, the angle, and the Connes-Størmer relative entropy for the pair of Hadamard subfactors are computed to understand their relative position. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conjugate pairs of Hadamard subfactors and vertex models Bakshi, Keshab Chandra Guin, Satyajit Guruprasad Operator Algebras Functional Analysis 46L37, 46L55, 46L10, 37A35 We show that any two Hadamard subfactors arising from a pair of distinct complex Hadamard matrices of order 3 are either equal or conjugate by a unitary in the relative commutant of their intersection. Moreover, when the Hadamard subfactors are not equal, we prove the factoriality of their intersection, and it turns out to be a vertex model subfactor. We compute the first relative commutant and characterize this subfactor by identifying it with a particular type of Krishnan-Sunder subfactor. A few key invariants, including the Pimsner-Popa probabilistic number, the angle, and the Connes-Størmer relative entropy for the pair of Hadamard subfactors are computed to understand their relative position. |
| title | Conjugate pairs of Hadamard subfactors and vertex models |
| topic | Operator Algebras Functional Analysis 46L37, 46L55, 46L10, 37A35 |
| url | https://arxiv.org/abs/2401.01664 |