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Sur certaines classes d’algèbres de Lie rigides. (On some classes of rigid Lie algebras). (French) Zbl 0559.17010
This work proposes minorations of the number of open orbits (solvable and non-solvable) in the variety \(L_ m\) of m-dimensional Lie algebras. These minorants increase very fastly with m in spite of the restrictive conditions imposed to the tested family of Lie algebras. We give then a series of solvable and rigid Lie algebras which do not annihilate the second adjoint cohomology group. The quadratic application of Rim is zero for this series. This implies that the variety \(L_ m\) is not reduced (if \(m\geq 13)\) for its scheme structure defined by the Jacobi rules.

17B99 Lie algebras and Lie superalgebras
17B30 Solvable, nilpotent (super)algebras
17B05 Structure theory for Lie algebras and superalgebras
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