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Some 2-step nilpotent Lie algebras. I. (English) Zbl 0992.17005

In the paper under review, one describes properties of some classes of completable 2-step nilpotent Lie algebras. A complex finite-dimensional nilpotent Lie algebra is said to be completable if its semidirect product with a maximal torus of derivations is a complete Lie algebra, in the sense that it is centerless and all its derivations are inner.
Every direct sum of Heisenberg algebras is completable (Theorem 3), and its derivation algebra is complete (Theorem 7). Other results concerning completable 2-step nilpotent Lie algebras are formulated by means of the notion of a minimal system of generators (introduced in Definitions 2 and 5).

MSC:

17B30 Solvable, nilpotent (super)algebras
17B05 Structure theory for Lie algebras and superalgebras
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