{"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":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"28 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Edinburgh Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0013091524000324","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.
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