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Singularities of solutions, spectral sequences and normal forms of Lie algebras of vector fields. (Russian) Zbl 0643.58039
This paper gives a general method of finding conditions of formal solvability of systems of differential equations in a class of functions with singularities. The author investigates here a formal linearization of an action of Lie algebra of vector fields; in particular the algebras of contact and Hamiltonian vector fields are considered. For a semisimple, reductive or commutative Lie algebra he obtains conditions for a formal equivalence to imply a \(C^{\infty}\)- or \(C^{\omega}\)- equivalence.
The results of this paper were announced in Dokl. Akad. Nauk SSSR 251, 794-799 (1980; Zbl 0475.58026) and Usp. Mat. Nauk 38, No.5(233), 199-200 (1983; Zbl 0552.58008).
Reviewer: W.Mozgawa

58J99 Partial differential equations on manifolds; differential operators
17B65 Infinite-dimensional Lie (super)algebras
17B56 Cohomology of Lie (super)algebras