Singularities of solutions, spectral sequences and normal forms of Lie algebras of vector fields. (Russian) Zbl 0643.58039

Lychagin, V. V.

Izv. Akad. Nauk SSSR, Ser. Mat. 51, No. 3, 584-612 (1987).

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

MSC:

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

Keywords:

spectral sequence; cohomology of Lie algebra; Gel’fand-Fuks cohomology; formal solvability