{"title":"复杂环上的非定常李代数分类","authors":"Vincent Knibbeler, Sara Lombardo, Casper Oelen","doi":"10.1017/s0013091524000324","DOIUrl":null,"url":null,"abstract":"We classify the automorphic Lie algebras of equivariant maps from a complex torus to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091524000324_inline1.png\"/> <jats:tex-math>$\\mathfrak{sl}_2(\\mathbb{C})$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. For each case, we compute a basis in a normal form. The automorphic Lie algebras correspond precisely to two disjoint families of Lie algebras parametrised by the modular curve of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091524000324_inline2.png\"/> <jats:tex-math>$\\mathrm{PSL}_2({\\mathbb{Z}})$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, apart from four cases, which are all isomorphic to Onsager’s algebra.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A classification of automorphic Lie algebras on complex tori\",\"authors\":\"Vincent Knibbeler, Sara Lombardo, Casper Oelen\",\"doi\":\"10.1017/s0013091524000324\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We classify the automorphic Lie algebras of equivariant maps from a complex torus to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" mimetype=\\\"image\\\" xlink:href=\\\"S0013091524000324_inline1.png\\\"/> <jats:tex-math>$\\\\mathfrak{sl}_2(\\\\mathbb{C})$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. For each case, we compute a basis in a normal form. The automorphic Lie algebras correspond precisely to two disjoint families of Lie algebras parametrised by the modular curve of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" mimetype=\\\"image\\\" xlink:href=\\\"S0013091524000324_inline2.png\\\"/> <jats:tex-math>$\\\\mathrm{PSL}_2({\\\\mathbb{Z}})$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, apart from four cases, which are all isomorphic to Onsager’s algebra.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0013091524000324\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0013091524000324","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A classification of automorphic Lie algebras on complex tori
We classify the automorphic Lie algebras of equivariant maps from a complex torus to $\mathfrak{sl}_2(\mathbb{C})$. For each case, we compute a basis in a normal form. The automorphic Lie algebras correspond precisely to two disjoint families of Lie algebras parametrised by the modular curve of $\mathrm{PSL}_2({\mathbb{Z}})$, apart from four cases, which are all isomorphic to Onsager’s algebra.
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