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Sbornik: Mathematics, 2009, Volume 200, Issue 8, Pages 1149–1164
DOI: https://doi.org/10.1070/SM2009v200n08ABEH004032
(Mi sm6383)
 

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
References:
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
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 8, Pages 45–62
DOI: https://doi.org/10.4213/sm6383
Bibliographic databases:
UDC: 514.763.8
MSC: Primary 37J15; Secondary 37J35, 53D20
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2009v200n08ABEH004032
  • https://www.mathnet.ru/eng/sm/v200/i8/p45
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математический сборник Sbornik: Mathematics
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    Russian version PDF:277
    English version PDF:16
    References:67
    First page:10
     
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