English

Automorphic Lie algebras and corresponding integrable systems

Exactly Solvable and Integrable Systems 2020-10-23 v1

Abstract

We study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are infinite dimensional and almost graded. We formulate the concept of a graded isomorphism and classify sl(2,C)sl(2,C) based automorphic Lie algebras corresponding to all finite reduction groups. We show that hierarchies of integrable systems, their Lax representations and master symmetries can be naturally formulated in terms of automorphic Lie algebras.

Keywords

Cite

@article{arxiv.2010.11316,
  title  = {Automorphic Lie algebras and corresponding integrable systems},
  author = {Rhys T. Bury and Alexander V. Mikhailov},
  journal= {arXiv preprint arXiv:2010.11316},
  year   = {2020}
}
R2 v1 2026-06-23T19:32:11.395Z