This article is cited in 14 papers

Integrable Hamiltonian systems on low-dimensional Lie algebras

A. A. Korotkevich

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: For any real Lie algebra of dimension 3, 4 or 5 and any nilpotent algebra of dimension 6 an integrable Hamiltonian system with polynomial coefficients is found on its coalgebra. These systems are constructed using Sadetov's method for constructing complete commutative families of polynomials on a Lie coalgebra.
Bibliography: 17 titles.

Keywords: integrable Hamiltonian systems, complete commutative families of polynomials, Sadetov's method.

UDC: 514.745.8

MSC: Primary 37J35; Secondary 70H06, 17B05

Received: 13.03.2009

DOI: 10.4213/sm7556

 English version: Sbornik: Mathematics, 2009, 200:12, 1731–1766

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