Twisted bimodules and associative algebras associated to VOAs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908694934978560 |
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| author | Xu, Shun |
| author_facet | Xu, Shun |
| contents | Let $V$ be a vertex operator algebra, $g$ be an automorphism of $V$ of order $T$, and $m, n \in (1/T)\mathbb{N}$. In~\cite{HX2} and~\cite{HXX1}, it was shown respectively that the associative algebra $A_{g,n}(V)$ constructed by Dong, Li, and Mason~\cite{DLM3}, and the $A_{g,n}(V)\!-\!A_{g,m}(V)$-bimodule $A_{g,n,m}(V)$ constructed by Dong and Jiang~\cite{DJ2}, are both isomorphic to certain subquotients of $U(V[g])$, where $U(V[g])$ denotes the universal enveloping algebra of $V$ with respect to $g$. In this paper, we give a unified and concise proof of these isomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisted bimodules and associative algebras associated to VOAs Xu, Shun Quantum Algebra 17B69 Let $V$ be a vertex operator algebra, $g$ be an automorphism of $V$ of order $T$, and $m, n \in (1/T)\mathbb{N}$. In~\cite{HX2} and~\cite{HXX1}, it was shown respectively that the associative algebra $A_{g,n}(V)$ constructed by Dong, Li, and Mason~\cite{DLM3}, and the $A_{g,n}(V)\!-\!A_{g,m}(V)$-bimodule $A_{g,n,m}(V)$ constructed by Dong and Jiang~\cite{DJ2}, are both isomorphic to certain subquotients of $U(V[g])$, where $U(V[g])$ denotes the universal enveloping algebra of $V$ with respect to $g$. In this paper, we give a unified and concise proof of these isomorphisms. |
| title | Twisted bimodules and associative algebras associated to VOAs |
| topic | Quantum Algebra 17B69 |
| url | https://arxiv.org/abs/2512.05605 |