an:04048726
Zbl 0643.58039
Lychagin, V. V.
Singularities of solutions, spectral sequences and normal forms of Lie algebras of vector fields
RU
Izv. Akad. Nauk SSSR, Ser. Mat. 51, No. 3, 584-612 (1987).
00166507
1987
j
58J99 17B65 17B56
spectral sequence; cohomology of Lie algebra; Gel'fand-Fuks cohomology; formal solvability
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).
W.Mozgawa
Zbl 0475.58026; Zbl 0552.58008