Maximally homogeneous G-structures and filtered Lie algebras. (English. Russian original) Zbl 0695.17011

Alekseevskij, D. V.

Sov. Math., Dokl. 37, No. 2, 381-384 (1988); translation from Dokl. Akad. Nauk SSSR 299, No. 3, 521-525 (1988).

The author obtains a description of filtered Lie algebras \({\mathfrak L}\) whose graduation equals the full Cartan extension of the Lie algebra \({\mathfrak g}\), under the additional assumption that \({\mathfrak L}\) satisfies a generalized Kantor-Tanaka reductivity condition. The description is given in terms of invariant Spencer cohomology. Some consequences for the theory of G-structures are obtained.

Reviewer: I.V.Chekalov

MSC:

17B70	Graded Lie (super)algebras
17B45	Lie algebras of linear algebraic groups
53C10	\(G\)-structures
53C30	Differential geometry of homogeneous manifolds

Keywords:

graded Lie algebras; filtered Lie algebras; G-structures