Abstract:
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.
\Bibitem{Vor09}
\by A.~S.~Vorontsov
\paper Invariants of Lie algebras representable as semidirect sums with a~commutative ideal
\jour Sb. Math.
\yr 2009
\vol 200
\issue 8
\pages 1149--1164
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Linking options:
https://www.mathnet.ru/eng/sm6383
https://doi.org/10.1070/SM2009v200n08ABEH004032
https://www.mathnet.ru/eng/sm/v200/i8/p45
This publication is cited in the following 3 articles:
Podobryaev A.V., “Casimir Functions of Free Nilpotent Lie Groups of Steps 3 and 4”, J. Dyn. Control Syst., 27:4 (2021), 625–644
K. S. Vorushilov, “Jordan–Kronecker invariants of semidirect sums of the form $\mathrm{sl}(n)+(\mathbb R^{n})^k$ and $\mathrm{gl}(n)+(\mathbb R^{n})^k$”, J. Math. Sci., 259:5 (2021), 571–582
Vorushilov K., “Jordan-Kronecker Invariants For Semidirect Sums Defined By Standard Representation of Orthogonal Or Symplectic Lie Algebras”, Lobachevskii J. Math., 38:6 (2017), 1121–1130
Citation in format AMSBIB
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