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.

36 pages. To appear in the Proceedings of the Edinburgh Mathematical Society

References in corpus (3)

• Automorphic Lie Algebras with dihedral symmetry
• Wild Local Structures of Automorphic Lie Algebras
• Polyhedral Groups in $G_2(\mathbb{C})$

Cited by in corpus (1)

• Computing equivariant matrices on homogeneous spaces for Geometric Deep Learning and Automorphic Lie Algebras