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Mat. Zametki, 2009, Volume 86, Issue 1, Pages 3–13 (Mi mz5704)  

This article is cited in 5 scientific papers (total in 5 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

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

DOI: https://doi.org/10.4213/mzm5704

Full text: PDF file (499 kB)
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English version:
Mathematical Notes, 2009, 86:1, 10–18

Bibliographic databases:

UDC: 514.74+512.815
Received: 23.07.2008
Revised: 29.11.2008

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Maslov, “Fluid thermodynamics: Qualitative consideration”, Theoret. and Math. Phys., 161:2 (2009), 1513–1528  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. Yu. Konyaev, “Bifurcation diagram and the discriminant of a spectral curve of integrable systems on Lie algebras”, Sb. Math., 201:9 (2010), 1273–1305  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Math. Notes, 90:5 (2011), 666–677  mathnet  crossref  crossref  mathscinet  isi
    4. Bolsinov A.V., Zhang P., “Jordan-Kronecker Invariants of Finite-Dimensional Lie Algebras”, Transform. Groups, 21:1 (2016), 51–86  crossref  mathscinet  zmath  isi  scopus
    5. Bolsinov A., “Some Remarks About Mishchenko-Fomenko Subalgebras”, J. Algebra, 483 (2017), 58–70  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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