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Structure of perfect Lie algebras without center and outer derivations. (English) Zbl 0874.17002

Let \(L\) be a Lie algebra over the real or complex numbers which is perfect and complete. The author calls such an algebra sympathetic. He constructs a 25-dimensional example and shows that any sympathetic algebra can be decomposed uniquely into the sum of irreducible sympathetic ideals. He shows the existence of a maximal sympathetic ideal called the sympathetic radical and studies its properties which include a version of the Levi-Malcev Theorem. Many related results are shown in this paper.

MSC:

17B05 Structure theory for Lie algebras and superalgebras
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References:

[1] Angelopoulos, E.) .- Algèbres de Lie satisfaisant g = [g, g], Der(g) = adg, C.R. Acad. Sci.Paris, 306 (1988), pp. 523-525. · Zbl 0647.17006
[2] Angelopoulos, E.) and Benayadi, S.) .- Constructions d’algèbres de Lie sympathiques non semi-simples munies de produits scalaires invariants, C.R. Acad. Sci.Paris, 317 (1993), pp. 741-744. · Zbl 0823.17004
[3] Arnal, D.), Benamor, H.), Benayadi, S.) and Pinczon, G.) .- Une algèbre de Lie non semi-simple vérifiant H1 (g) = H2 (g) = H0 (g, g) = H1 (g, g) = H2 (g, g) = {0}, C.R. Acad. Sci.Paris, 315 (1992), pp. 261-263. · Zbl 0765.17005
[4] Benayadi, S.) .- Certaines propriétés d’une classe d’algèbres de Lie qui généralisent les algèbres de Lie semi-simples. Ann. Fac. Sci. Toulouse, Vol. XII, 1 (1991), pp. 29-35. · Zbl 0748.17006
[5] Benayadi, S.) Thèse, Université de Bourgogne1993.
[6] Bourbaki, N.) .- Groupes et algèbres de Lie, Hermann, Paris, chap. 1 (1971). · Zbl 0213.04103
[7] Simon, J.) Private communication.
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