dorsal/arxiv
View SchemaTwisted representations of vertex operator algebras
| Authors | Chongying Dong, Haisheng Li, Geoffrey Mason |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9509005 |
| URL | https://arxiv.org/abs/q-alg/9509005 |
Abstract
Let $V$ be a vertex operator algebra and $g$ an automorphism of finite order. We construct an associative algebra $A_g(V)$ and a pair of functors between the category of $A_g(V)$-modules and a certain category of admissible $g$-twisted $V$-modules. In particular, these functors exhibit a bijection between the simple modules in each category. We give various applications, including the fact that the complete reducibility of admissible $g$-twisted modules implies both the finite-dimensionality of homogeneous spaces and the finiteness of the number of simple $g$-twisted modules.
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"date_modified": "2026-03-02T18:01:25.373000Z",
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"abstract": "Let $V$ be a vertex operator algebra and $g$ an automorphism of finite order.\nWe construct an associative algebra $A_g(V)$ and a pair of functors between the\ncategory of $A_g(V)$-modules and a certain category of admissible $g$-twisted\n$V$-modules. In particular, these functors exhibit a bijection between the\nsimple modules in each category. We give various applications, including the\nfact that the complete reducibility of admissible $g$-twisted modules implies\nboth the finite-dimensionality of homogeneous spaces and the finiteness of the\nnumber of simple $g$-twisted modules.",
"arxiv_id": "q-alg/9509005",
"authors": [
"Chongying Dong",
"Haisheng Li",
"Geoffrey Mason"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Twisted representations of vertex operator algebras",
"url": "https://arxiv.org/abs/q-alg/9509005"
},
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