A classification of automorphic Lie algebras on complex tori
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.13598
- arXiv:
- arXiv:2405.13598
- Bibcode:
- 2024arXiv240513598K
- Keywords:
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- Mathematics - Rings and Algebras;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 36 pages. To appear in the Proceedings of the Edinburgh Mathematical Society