RT Book, Section
T1 On the rigidity of solvable Lie algebras
A1 Ancochea Bermúdez, José María
A2 Hazewinkel, Michiel
A2 Gerstenhaber, Murray
AB The author gives a method for the construction of solvable rigid Lie algebras in the varieties defined by Jacobi's identities. His method does not use tables of nilpotent Lie algebras and the rigidity is not obtained by usual cohomological criteria. He uses the fact that such an algebra g 0   is algebraic and has a Chevalley splitting T⊕n , where n  is the maximal nilpotent ideal and T  is a subalgebra constituted by ad g 0   -semisimple elements (by the adjoint representation ad g 0    we can also identify T  to a maximal torus of derivations over n) . The author takes a regular semisimple element X  (X∈T)  and studies all possible systems of relations (S) checked for the eigenvalues of the operator ad g 0  X . Certain systems (S) are not suitable and are directly eliminated. For the remaining cases, the rigidity is established by the method of perturbations in nonstandard analysis. As applications of his method the author gives a classification of solvable rigid Lie algebras of dimension ≤8  and a list of 48 rigid algebras in dimension 9.
PB Kluwer Academic
SN 90-277-2804-6
YR 1988
FD 1988
LK https://hdl.handle.net/20.500.14352/60682
UL https://hdl.handle.net/20.500.14352/60682
NO Papers from the NATO Advanced Study Institute held in Il Ciocco, June 1–14, 1986
DS Docta Complutense
RD 9 may 2024