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 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.
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}
}