Simple smooth modules over the Ramond algebra and applications to vertex operator superalgebras
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915199050579968 |
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| author | Chen, Yulu Yao, Yufeng Zhao, Kaiming |
| author_facet | Chen, Yulu Yao, Yufeng Zhao, Kaiming |
| contents | Simple smooth modules over the Virasoro algebra and one of the super-Virasoro algebras, named the Neveu-Schwarz algebra, have been classified. This problem remained unsolved for the other super-Virasoro algebra called the Ramond algebra.In this paper, all simple smooth modules over the Ramond algebra are classified. More precisely, we show that a simple smooth module over the Ramond algebra is either a simple highest weight module or isomorphic to an induced module from a simple module over a finite dimensional solvable Lie superalgebra.As an application we obtain all simple weak $ψ$-twisted modules over some vertex operator superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple smooth modules over the Ramond algebra and applications to vertex operator superalgebras Chen, Yulu Yao, Yufeng Zhao, Kaiming Representation Theory 17B65, 17B68, 17B69, 17B70, 81R10 Simple smooth modules over the Virasoro algebra and one of the super-Virasoro algebras, named the Neveu-Schwarz algebra, have been classified. This problem remained unsolved for the other super-Virasoro algebra called the Ramond algebra.In this paper, all simple smooth modules over the Ramond algebra are classified. More precisely, we show that a simple smooth module over the Ramond algebra is either a simple highest weight module or isomorphic to an induced module from a simple module over a finite dimensional solvable Lie superalgebra.As an application we obtain all simple weak $ψ$-twisted modules over some vertex operator superalgebras. |
| title | Simple smooth modules over the Ramond algebra and applications to vertex operator superalgebras |
| topic | Representation Theory 17B65, 17B68, 17B69, 17B70, 81R10 |
| url | https://arxiv.org/abs/2406.06388 |