A classification of automorphic Lie algebras on complex tori
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929597485940736 |
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| author | Knibbeler, Vincent Lombardo, Sara Oelen, Casper |
| author_facet | Knibbeler, Vincent Lombardo, Sara Oelen, Casper |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13598 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A classification of automorphic Lie algebras on complex tori Knibbeler, Vincent Lombardo, Sara Oelen, Casper Rings and Algebras Exactly Solvable and Integrable Systems 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. |
| title | A classification of automorphic Lie algebras on complex tori |
| topic | Rings and Algebras Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2405.13598 |