Benayadi, Said A new characterization of semisimple Lie algebras. (English) Zbl 0891.17005 Proc. Am. Math. Soc. 125, No. 3, 685-688 (1997). The author proves that a finite-dimensional quadratic Lie algebra over an algebraically closed field of characteristic 0 is semisimple if and only if its Casimir element is invertible. Reviewer: G.Brown (Boulder) Cited in 3 ReviewsCited in 6 Documents MSC: 17B20 Simple, semisimple, reductive (super)algebras 17B05 Structure theory for Lie algebras and superalgebras Keywords:semisimple Lie algebras; quadratic Lie algebras; Casimir elements PDFBibTeX XMLCite \textit{S. Benayadi}, Proc. Am. Math. Soc. 125, No. 3, 685--688 (1997; Zbl 0891.17005) Full Text: DOI References: [1] Saïd Benayadi, Une propriété nécessaire et suffisante pour qu’une algèbre de Lie sympathique quadratique soit semi-simple, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), no. 11, 1155 – 1158 (French, with English and French summaries). · Zbl 0814.17007 [2] Saïd Benayadi, Structures de certaines algèbres de Lie quadratiques, Comm. Algebra 23 (1995), no. 10, 3867 – 3887 (French). · Zbl 0835.17004 · doi:10.1080/00927879508825437 [3] N. Bourbaki, Éléments de mathématique. Fasc. XXVI. Groupes et algèbres de Lie. Chapitre I: Algèbres de Lie, Seconde édition. Actualités Scientifiques et Industrielles, No. 1285, Hermann, Paris, 1971 (French). · Zbl 0213.04103 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.