Wild Local Structures of Automorphic Lie Algebras

Duffield, Drew Damien; Knibbeler, Vincent; Lombardo, Sara

Abstract

We study automorphic Lie algebras using a family of evaluation maps parametrised by the representations of the associative algebra of functions. This provides a descending chain of ideals for the automorphic Lie algebra which is used to prove that it is of wild representation type. We show that the associated quotients of the automorphic Lie algebra are isomorphic to twisted truncated polynomial current algebras. When a simple Lie algebra is used in the construction, this allows us to describe the local Lie structure of the automorphic Lie algebra in terms of affine Kac-Moody algebras.

Citation

Duffield, D. D., Knibbeler, V., & Lombardo, S. (2024). Wild Local Structures of Automorphic Lie Algebras. Algebras and Representation Theory, 27(1), 305-331. https://doi.org/10.1007/s10468-023-10208-y

• Journal Article Type: Article
• Acceptance Date: Mar 21, 2023
• Online Publication Date: Jul 20, 2023
• Publication Date: Feb 1, 2024
• Deposit Date: Mar 26, 2024
• Publicly Available Date: Mar 26, 2024
• Journal: Algebras and Representation Theory
• Print ISSN: 1386-923X
• Electronic ISSN: 1572-9079
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 1
• Pages: 305-331
• DOI: https://doi.org/10.1007/s10468-023-10208-y
• Keywords: Truncated twisted current algebras, Automorphic Lie algebras, Equivariant map algebras, Compact Riemann surfaces, Representation type
• Public URL: https://durham-repository.worktribe.com/output/2313725