Completely integrable Hamiltonian systems on semidirect sums of Lie algebras

Journal Article · Tue Jun 30 04:00:00 EDT 2009 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2009V200N05ABEH004012; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21301606

Zhdanova, Maria M ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

The complete integrability of Hamiltonian systems arising on Lie algebras which have the form of a direct sum is investigated. For algebras in these classes Sadetov's method takes a simpler form: the isomorphism between the algebra arising at the second step of Sadetov's approach and the stationary subalgebra of a generic element can be written out explicitly. The explicit form of this isomorphism is presented, as well as explicit formulae for polynomials in complete systems for the algebras so(n)+(R{sup n}){sub k}, su(n)+(C{sup n}){sub k} and u(n)+(C{sup n}){sub k}. For the algebras so(n)+R{sup n} the degrees of the resulting polynomial functions are analysed. Bibliography: 15 titles.

• OSTI ID: 21301606
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 5 Vol. 200; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
ALGEBRA
HAMILTONIANS
INTEGRAL CALCULUS
LIE GROUPS
POLYNOMIALS