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