Cofiniteness for Twisted Fusion Products in Vertex Operator Algebra Theory
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909894323470336 |
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| author | Yang, Chao Zhu, Yiyi |
| author_facet | Yang, Chao Zhu, Yiyi |
| contents | Let $V$ be a vertex operator algebra equipped with two commuting finite-order automorphisms $g_1$ and $g_2$, and set $g_3 = g_1 g_2$. For $k = 1, 2, 3$, let $W^k$ be a $g_k$-twisted $V$-module. Assuming that $W^1$ and $W^2$ are $C_1$-cofinite and that there exists a surjective twisted logarithmic intertwining operator of type $\binom{W^3}{W^1 \ W^2}$, we prove that $W^3$ is also $C_1$-cofinite. The cofiniteness follows from the finite-dimensionality of the solution space of an associated complex-coefficient linear differential equation. As an application, under the condition of $C_1$-cofiniteness, we establish the finiteness of the fusion rules and construct the fusion product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06420 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cofiniteness for Twisted Fusion Products in Vertex Operator Algebra Theory Yang, Chao Zhu, Yiyi Quantum Algebra 17B69 Let $V$ be a vertex operator algebra equipped with two commuting finite-order automorphisms $g_1$ and $g_2$, and set $g_3 = g_1 g_2$. For $k = 1, 2, 3$, let $W^k$ be a $g_k$-twisted $V$-module. Assuming that $W^1$ and $W^2$ are $C_1$-cofinite and that there exists a surjective twisted logarithmic intertwining operator of type $\binom{W^3}{W^1 \ W^2}$, we prove that $W^3$ is also $C_1$-cofinite. The cofiniteness follows from the finite-dimensionality of the solution space of an associated complex-coefficient linear differential equation. As an application, under the condition of $C_1$-cofiniteness, we establish the finiteness of the fusion rules and construct the fusion product. |
| title | Cofiniteness for Twisted Fusion Products in Vertex Operator Algebra Theory |
| topic | Quantum Algebra 17B69 |
| url | https://arxiv.org/abs/2511.06420 |