On the Lie noncommutative integrability
Exactly Solvable and Integrable Systems
2026-02-19 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
The Lie theory of non-commutative integrability is used to reconstruct some integrable systems of ordinary differential equations in three dimensional Eucledian space. The Darboux-Brioschi-Halphen system is an example of the Lie integrable system associated with the simple Lie algebra sl(2,R). Other examples are related with solvable three dimensional real Lie algebras of Bianchi B class.
Cite
@article{arxiv.2602.16267,
title = {On the Lie noncommutative integrability},
author = {A. V. Tsiganov},
journal= {arXiv preprint arXiv:2602.16267},
year = {2026}
}
Comments
12 pages, LaTeX with Ams fonts