Geodesic
Invariants of Lie algebras representable as semidirect sums with a commutative ideal
Sbornik. Mathematics, Tome 200 (2009) no. 8, pp. 1149-1164 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $k$th 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.
Keywords: semisimple Lie algebras, commutative ideal, dynamical systems.
Mots-clés : invariants 
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A. S. Vorontsov. Invariants of Lie algebras representable as semidirect sums with a commutative ideal. Sbornik. Mathematics, Tome 200 (2009) no. 8, pp. 1149-1164. http://geodesic.mathdoc.fr/item/SM_2009_200_8_a2/

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