$C_{1}$-cofiniteness and vertex tensor categories
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912604219244544 |
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| author | Huang, Yi-Zhi |
| author_facet | Huang, Yi-Zhi |
| contents | We first generalize the logarithmic tensor category theory of Huang-Lepowsky-Zhang to the more general case that the module category for a vertex operator algebra $V$ (more generally a Möbius vertex algebra) might not be closed under the contragredient functor. Then by verifying the assumptions to use this generalization, we obtain that (logarithmic) intertwining operators among $C_{1}$-cofinite grading-restricted generalized $V$-modules satisfy the associativity property (operator product expansion) and the category of $C_{1}$-cofinite grading-restricted generalized $V$-modules has a natural vertex tensor category structure. In particular, this category has a natural braided tensor category structure with a twist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C_{1}$-cofiniteness and vertex tensor categories Huang, Yi-Zhi Quantum Algebra 17B69, 18M15, 81T40 We first generalize the logarithmic tensor category theory of Huang-Lepowsky-Zhang to the more general case that the module category for a vertex operator algebra $V$ (more generally a Möbius vertex algebra) might not be closed under the contragredient functor. Then by verifying the assumptions to use this generalization, we obtain that (logarithmic) intertwining operators among $C_{1}$-cofinite grading-restricted generalized $V$-modules satisfy the associativity property (operator product expansion) and the category of $C_{1}$-cofinite grading-restricted generalized $V$-modules has a natural vertex tensor category structure. In particular, this category has a natural braided tensor category structure with a twist. |
| title | $C_{1}$-cofiniteness and vertex tensor categories |
| topic | Quantum Algebra 17B69, 18M15, 81T40 |
| url | https://arxiv.org/abs/2509.20737 |