Invariants of Lie algebras representable as semidirect sums with a commutative ideal
- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
Explicit formulae for invariants of the coadjoint representation are presented for Lie algebras that are semidirect sums of a classical semisimple Lie algebra with a commutative ideal with respect to a representation of minimal dimension or to a kth tensor power of such a representation. These formulae enable one to apply some known constructions of complete commutative families and to compare integrable systems obtained in this way. A completeness criterion for a family constructed by the method of subalgebra chains is suggested and a conjecture is formulated concerning the equivalence of the general Sadetov method and a modification of the method of shifting the argument, which was suggested earlier by Brailov. Bibliography: 12 titles.
- OSTI ID:
- 21301529
- Journal Information:
- Sbornik. Mathematics, Vol. 200, Issue 8; Other Information: DOI: 10.1070/SM2009v200n08ABEH004032; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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