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On a family of ideally finite Lie algebras. (Sur une famille d’algèbres de Lie idéalement finies.) (French) Zbl 0867.17005

Ideally finite Lie algebras are those generated by finite-dimensional ideals. The author considers the case when these ideals are complete and perfect. This condition is shown to be equivalent to the algebra being the direct sum of finite-dimensional, complete, perfect and irreducible ideals. A radical related to this concept is introduced and developed for ideally finite Lie algebras.

MSC:

17B05 Structure theory for Lie algebras and superalgebras
17B65 Infinite-dimensional Lie (super)algebras
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References:

[1] Angelopoulos, E., C.R. Acad. Sci. Paris, t. 306, série I, 1988, p. 523-525. · Zbl 0647.17006
[2] 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, N 1, 1991, p. 29-35. · Zbl 0748.17006
[3] Benayadi, S., Structure of perfect Lie algebras without center and outer derivations, Ann. Fac. Sci. Toulouse (à paraître). · Zbl 0874.17002
[4] Bourbaki, N., Groupes et algèbres de Lie, ch. 1, Hermann, Paris. 1971. · Zbl 0249.54001
[5] Stewart, I.N., Lie algebras generated by finite-dimensional ideals. Pitman Publishing, London, 1975. · Zbl 0325.17002
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