Classification of unsolvable Lie algebras with four-dimensional orbits of coadjoint representation

F. I. Lobzin<sup>ab

a</sup> Moscow Center of Fundamen tal and Applied Mathematics (Moscow)
^b Lomonosov Moscow State University (Moscow)

Abstract: The paper presents a classification of Lie algebras with four-dimensional coadjoint orbits for Lie algebras that are isomorphic to a semidirect sum of a nontrivial semisimple Lie algebra and a nonzero solvable ideal.

Keywords: Poisson bracket, Lie algebra, coadjoint representation, integrable systems.

UDC: 514.747.2

Received: 12.02.2025
Accepted: 07.04.2025

DOI: 10.22405/2226-8383-2025-26-2-141-159