Wild Local Structures of Automorphic Lie Algebras

Drew Damien Duffield, Vincent Knibbeler, Sara Lombardo*

*Corresponding author for this work

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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.

Original languageEnglish
Pages (from-to)305-331
Number of pages27
JournalAlgebras and Representation Theory
Volume27
Issue number1
Early online date20 Jul 2023
DOIs
Publication statusPublished - Feb 2024

Keywords

  • Automorphic Lie algebras
  • Compact Riemann surfaces
  • Equivariant map algebras
  • Representation type
  • Truncated twisted current algebras

ASJC Scopus subject areas

  • General Mathematics

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