Twisted intertwining operators and tensor products of (generalized) twisted modules
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913929023717376 |
|---|---|
| author | Du, Jishen Huang, Yi-Zhi |
| author_facet | Du, Jishen Huang, Yi-Zhi |
| contents | We study the general twisted intertwining operators (intertwining operators among twisted modules) for a vertex operator algebra $V$. We give the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators and also prove some other properties of twisted intertwining operators. Using twisted intertwining operators, we introduce a notion of $P(z)$-tensor product of two objects for $z\in \mathbb{C}^{\times}$ in a category of suitable $g$-twisted $V$-modules for $g$ in a group of automorphisms of $V$ and give a construction of such a $P(z)$-tensor product under suitable assumptions. We also construct $G$-crossed commutativity isomorphisms and $G$-crossed braiding isomorphisms. We formulate a $P(z)$-compatibility condition and a $P(z)$-grading-restriction condition and use these conditions to give another construction of the $P(z)$-tensor product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisted intertwining operators and tensor products of (generalized) twisted modules Du, Jishen Huang, Yi-Zhi Quantum Algebra High Energy Physics - Theory 17B69, 18M15, 81T40 We study the general twisted intertwining operators (intertwining operators among twisted modules) for a vertex operator algebra $V$. We give the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators and also prove some other properties of twisted intertwining operators. Using twisted intertwining operators, we introduce a notion of $P(z)$-tensor product of two objects for $z\in \mathbb{C}^{\times}$ in a category of suitable $g$-twisted $V$-modules for $g$ in a group of automorphisms of $V$ and give a construction of such a $P(z)$-tensor product under suitable assumptions. We also construct $G$-crossed commutativity isomorphisms and $G$-crossed braiding isomorphisms. We formulate a $P(z)$-compatibility condition and a $P(z)$-grading-restriction condition and use these conditions to give another construction of the $P(z)$-tensor product. |
| title | Twisted intertwining operators and tensor products of (generalized) twisted modules |
| topic | Quantum Algebra High Energy Physics - Theory 17B69, 18M15, 81T40 |
| url | https://arxiv.org/abs/2501.15003 |