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Spectral sequences and normal forms of Lie algebras of vector fields. (English. Russian original) Zbl 0552.58008
Russ. Math. Surv. 38, No. 5, 152-153 (1983); translation from Usp. Mat. Nauk 38, No. 5(233), 199-200 (1983).
Given a representation \(\alpha\) of a Lie algebra \({\mathcal G}\) into the Lie algebra \({\mathcal D}\) of vector fields together with a suitable filtration of \({\mathcal D}\), the author constructs a spectral sequence which allows one to calculate a normal form for the elements of \(\alpha\) (\({\mathcal G})\) near their elementary critical points. This results applies, for example, when \({\mathcal G}\) is the Lie algebra of Hamiltonian (resp. contact) vector fields on a symplectic (resp. contact) manifold.
Reviewer: D.McDuff

MSC:
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
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