Invariants of Lie algebras representable as semidirect sums with a commutative ideal

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.