A classification of automorphic Lie algebras on complex tori

Vincent Knibbeler; Sara Lombardo; Casper Oelen

doi:10.1017/S0013091524000324

A classification of automorphic Lie algebras on complex tori

Vincent Knibbeler, Sara Lombardo, Casper Oelen

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Abstract

We classify the automorphic Lie algebras of equivariant maps from a complex torus to 𝔰𝔩₂(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 PSL₂(ℤ), apart from four cases, which are all isomorphic to Onsager’s algebra.

Original language	English
Pages (from-to)	1-43
Number of pages	43
Journal	Proceedings of the Edinburgh Mathematical Society
Early online date	28 May 2024
DOIs	https://doi.org/10.1017/S0013091524000324
Publication status	E-pub ahead of print - 28 May 2024

Keywords

rings and algebras
infinite-dimensional Lie algebras
equivariant map algebras
automorphic Lie algebras

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KW - infinite-dimensional Lie algebras

KW - equivariant map algebras

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A classification of automorphic Lie algebras on complex tori

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