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

M. V. Karasev

Izvestiya. Mathematics , Tome 28 (1987) no. 3, pp. 497-527.

Résumé

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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