Some 2-step nilpotent Lie algebras. I (Q5955649)
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scientific article; zbMATH DE number 1705644
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some 2-step nilpotent Lie algebras. I |
scientific article; zbMATH DE number 1705644 |
Statements
Some 2-step nilpotent Lie algebras. I (English)
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1 July 2002
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derivation
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2-step nilpotent Lie algebras
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root space decomposition
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complete Lie algebra
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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. NEWLINENEWLINENEWLINEEvery 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).
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