Geodesic
On the intersection of irreducible components of the space of finite-dimensional Lie algebras
Sbornik. Mathematics, Tome 203 (2012) no. 7, pp. 976-995

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The irreducible components of the space of $n$-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra is considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.
Keywords: Lie algebra, space of Lie algebras, irreducible component, nilpotent Lie algebra. 
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     author = {V. V. Gorbatsevich},
     title = {On the intersection of irreducible components of the space of finite-dimensional {Lie} algebras},
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     number = {7},
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V. V. Gorbatsevich. On the intersection of irreducible components of the space of finite-dimensional Lie algebras. Sbornik. Mathematics, Tome 203 (2012) no. 7, pp. 976-995. http://geodesic.mathdoc.fr/item/SM_2012_203_7_a2/