Solvable quadratic Lie algebras in low dimensions. (English) Zbl 1285.17005
In this paper the authors classify solvable quadratic complex Lie algebras up to dimension six. Although the classification up to dimension five is known (see e.g. [F. Zhu and Z. Chen, J. Phys. A, Math. Theor. 40, No. 47, 14243–14251 (2007; Zbl 1127.17002)]), in this paper the result is obtained by a different procedure, based principally on the Witt decomposition, the double extension method and properties of graded structures. The three families resulting in dimension six are shown to be non \(i\)-isomorphic, hence non-isomorphic.
Reviewer: Rutwig Campoamor-Stursberg (Madrid)
MSC:
17B05 | Structure theory for Lie algebras and superalgebras |
17B30 | Solvable, nilpotent (super)algebras |
17B40 | Automorphisms, derivations, other operators for Lie algebras and super algebras |