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This article is cited in 3 scientific papers (total in 3 papers)
Invariants of Lie algebras representable as semidirect sums with a commutative ideal
A. S. Vorontsov M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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.
Keywords:
semisimple Lie algebras, commutative ideal, invariants, dynamical systems.
Received: 19.06.2008 and 20.02.2009
Citation:
A. S. Vorontsov, “Invariants of Lie algebras representable as semidirect sums with a commutative ideal”, Mat. Sb., 200:8 (2009), 45–62; Sb. Math., 200:8 (2009), 1149–1164
Linking options:
https://www.mathnet.ru/eng/sm6383https://doi.org/10.1070/SM2009v200n08ABEH004032 https://www.mathnet.ru/eng/sm/v200/i8/p45
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Abstract page: | 537 | Russian version PDF: | 277 | English version PDF: | 16 | References: | 67 | First page: | 10 |
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