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On the rigidity of solvable Lie algebras. (English) Zbl 0672.17006
Deformation theory of algebras and structures and applications, NATO Adv. Study Inst., Castelvecchio-Pascoli/Italy 1986, NATO ASI Ser., Ser. C 247, 403-445 (1988).
[For the entire collection see Zbl 0654.00006.]
Low dimensional solvable Lie algebras with open orbit are studied. The method used is the study of the rank of a linear system associated to an adjoint diagonal operator. In the construction the following fact used is: If \(L\) is a rigid Lie algebra, then there exists a non-trivial maximal torus of inner derivations. The method allows to decide about the rigidity of a given solvable Lie algebra. Of course, in dimension greater than 8 there is no classification theorem.
MSC:
17B30 Solvable, nilpotent (super)algebras
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
Citations:
Zbl 0654.00006