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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 3, Pages 508–538 (Mi izv1499)  

This article is cited in 35 scientific papers (total in 35 papers)

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

M. V. Karasev

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.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:3, 497–527

Bibliographic databases:

UDC: 517.9
MSC: Primary 58F05; Secondary 22E70, 81C25
Received: 22.02.1984
Revised: 20.01.1986

Citation: M. V. Karasev, “Analogues of the objects of Lie group theory for nonlinear Poisson brackets”, Izv. Akad. Nauk SSSR Ser. Mat., 50:3 (1986), 508–538; Math. USSR-Izv., 28:3 (1987), 497–527

Citation in format AMSBIB
\by M.~V.~Karasev
\paper Analogues of the objects of Lie group theory for nonlinear Poisson brackets
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 3
\pages 508--538
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 3
\pages 497--527

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    2. A WEINSTEIN, “Connections of Berry and Hannay type for moving Lagrangian submanifolds”, Advances in Mathematics, 82:2 (1990), 133  crossref
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