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Mathematics of the USSR-Izvestiya, 1987, Volume 28, Issue 3, Pages 497–527
DOI: https://doi.org/10.1070/IM1987v028n03ABEH000895 (Mi im1499) 		 
This article is cited in 68 scientific papers (total in 68 papers)

Analogues of the objects of Lie group theory for nonlinear Poisson brackets

M. V. Karasev
English version PDF (1853 kB) Citations (68) Russian version article
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DOI: https://doi.org/10.1070/IM1987v028n03ABEH000895
Abstract: For general degenerate Poisson brackets, analogues are constructed of invariant vector fields, invariant forms, Haar measure and adjoint representation. A pseudogroup operation is defined that corresponds to nonlinear Poisson brackets, and analogues are obtained for the three classical theorems of Lie. The problem of constructing global pseudogroups is examined.
Bibliography: 49 titles.
Received: 22.02.1984
Revised: 20.01.1986
Bibliographic databases:
UDC: 517.9
MSC: Primary 58F05; Secondary 22E70, 81C25
Language: English
Original paper language: Russian
Citation: M. V. Karasev, “Analogues of the objects of Lie group theory for nonlinear Poisson brackets”, Math. USSR-Izv., 28:3 (1987), 497–527
Citation in format AMSBIB
\Bibitem{Kar86}
\by M.~V.~Karasev
\paper Analogues of the objects of Lie group theory for nonlinear Poisson brackets
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 3
\pages 497--527
\mathnet{http://mi.mathnet.ru//eng/im1499}
\crossref{https://doi.org/10.1070/IM1987v028n03ABEH000895}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=854594}
\zmath{https://zbmath.org/?q=an:0624.58007|0608.58023}
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    • This publication is cited in the following 68 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:812
    Russian version PDF:312
    English version PDF:39
    References:95
    First page:2
     
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