Braided tensor product of von Neumann algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910759911424000 |
|---|---|
| author | De Commer, Kenny Krajczok, Jacek |
| author_facet | De Commer, Kenny Krajczok, Jacek |
| contents | We introduce a definition of braided tensor product $\operatorname{M}\overline{\boxtimes}\operatorname{N}$ of von Neumann algebras equipped with an action of a quasi-triangular quantum group $\mathbb{G}$ (this includes the case when $\mathbb{G}$ is a Drinfeld double). It is a new von Neumann algebra which comes together with embeddings of $\operatorname{M},\operatorname{N}$ and the unique action of $\mathbb{G}$ for which embeddings are equivariant. More generally, we construct braided tensor product of von Neumann algebras equipped with actions of locally compact quantum groups linked by a bicharacter. We study several examples, in particular we show that crossed products can be realised as braided tensor products. We also show that one can take the braided tensor product $\vartheta_1\boxtimes\vartheta_2$ of normal, completely bounded maps which are equivariant, but this fails without the equivariance condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17444 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Braided tensor product of von Neumann algebras De Commer, Kenny Krajczok, Jacek Operator Algebras Functional Analysis Quantum Algebra We introduce a definition of braided tensor product $\operatorname{M}\overline{\boxtimes}\operatorname{N}$ of von Neumann algebras equipped with an action of a quasi-triangular quantum group $\mathbb{G}$ (this includes the case when $\mathbb{G}$ is a Drinfeld double). It is a new von Neumann algebra which comes together with embeddings of $\operatorname{M},\operatorname{N}$ and the unique action of $\mathbb{G}$ for which embeddings are equivariant. More generally, we construct braided tensor product of von Neumann algebras equipped with actions of locally compact quantum groups linked by a bicharacter. We study several examples, in particular we show that crossed products can be realised as braided tensor products. We also show that one can take the braided tensor product $\vartheta_1\boxtimes\vartheta_2$ of normal, completely bounded maps which are equivariant, but this fails without the equivariance condition. |
| title | Braided tensor product of von Neumann algebras |
| topic | Operator Algebras Functional Analysis Quantum Algebra |
| url | https://arxiv.org/abs/2412.17444 |