ANALOGUES OF THE OBJECTS OF LIE GROUP THEORY FOR NONLINEAR POISSON BRACKETS

1987/06/30 by M. V. Karasev · 3 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Black Holes and Theoretical Physics #Advanced Topics in Algebra

paper · doi:10.1070/im1987v028n03abeh000895

openalex publication_date 1987/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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.

Citations

• The Principles of Quantum Mechanics
• Generalized Liouville method of integration of Hamiltonian systems
• Fourier integral operators. I

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• Feuilletages en surfaces, cycles �vanouissants et vari�t�s de Poisson
• Poisson structures on double Lie groups
• Poisson manifold [wikipedia]