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Matematicheskie Zametki, 2009, Volume 86, Issue 1, Pages 3–13
DOI: https://doi.org/10.4213/mzm5704 (Mi mzm5704) 		 
This article is cited in 6 scientific papers (total in 6 papers)

A Formal Frobenius Theorem and Argument Shift

A. V. Bolsinovab, K. M. Zueva

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Loughborough University
Full-text PDF (499 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm5704
Abstract: A formal Frobenius theorem, which is an analog of the classical integrability theorem for smooth distributions, is proved and applied to generalize the argument shift method of A. S. Mishchenko and A. T. Fomenko to finite-dimensional Lie algebras over any field of characteristic zero. A completeness criterion for a commutative set of polynomials constructed by the formal argument shift method is obtained.
Keywords: formal Frobenius theorem, argument shift, finite-dimensional Lie algebra, complete commutative set of polynomials.
Received: 23.07.2008
Revised: 29.11.2008
English version:
Mathematical Notes, 2009, Volume 86, Issue 1, Pages 10–18
DOI: https://doi.org/10.1134/S0001434609070025
Bibliographic databases:
UDC: 514.74+512.815
Language: Russian
Citation: A. V. Bolsinov, K. M. Zuev, “A Formal Frobenius Theorem and Argument Shift”, Mat. Zametki, 86:1 (2009), 3–13; Math. Notes, 86:1 (2009), 10–18
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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