Carles, R.; Diakité, Y. Sur les variétés d’algèbres de Lie de dimension \(\leq 7\). (French) Zbl 0546.17006 J. Algebra 91, 53-63 (1984). The varieties \(L_ m\) of Lie algebra structures of dimension \(m\leq 7\) over an algebraically closed field K, char K\(=0\), are studied. Using the known classification of nilpotent Lie algebras of dimension \(\leq 6\) and the density of the decomposable Lie algebra laws, the authors determine all the irreducible components and open orbits of the varieties \(L_ m\). Reviewer: S.Prishchepionok Cited in 2 ReviewsCited in 27 Documents MSC: 17B99 Lie algebras and Lie superalgebras 17B05 Structure theory for Lie algebras and superalgebras 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras Keywords:varieties of Lie algebras; characteristic zero; nilpotent radical; irreducible components; open orbits Citations:Zbl 0427.17013 PDFBibTeX XMLCite \textit{R. Carles} and \textit{Y. Diakité}, J. Algebra 91, 53--63 (1984; Zbl 0546.17006) Full Text: DOI References: [1] Bourbaki, N., Groupes et algèbres de Lie, I (1971), Hermann: Hermann Paris · Zbl 0213.04103 [2] Carles, R., C. R. Acad. Sci. Paris, 289, 263 (1979) [3] Carles, R., C. R. Acad. Sci. Paris, 293, 545 (1981) [4] Diakité, Y., Thèse de 3ème cycle (1979), notes non publiées [5] Hochschild, G.; Serre, J.-P, Cohomology of Lie algebras, Ann. of Math., 57, 591 (1953) · Zbl 0053.01402 [6] Morosov, V. V., Isv. Vysš. Učebn Zaved. Mathematika A, 190, 161 (1958) [7] Rauch, G., Effacement et déformation, Ann. Inst. Fourier (Grenoble), 22, No. 1, 239 (1972) · Zbl 0219.17006 [8] Richardson, R. W., Pacific J. Math., 22, No. 2, 339 (1967) [9] Umlauf, K. A., Doctorat (1891), Leipzig [10] Vergne, M., Thèse 3ème cycle (1966), Paris 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.