## 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
Full Text:

### 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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.