Abstract
In this paper we develop a method of construction of complex rigid solvable Lie algebras which is independent of coho-mological techniques or classification of Lie algebras. As an application, we classify all rigid solvable Lie algebras in dimension less or equal than eight, and we obtain partial results in dimension nine. Moreover, we give several examples of families of rigid Lie algebras in arbitrary dimension, some of them having its second cohomology group, in the Chevalley cohomology, non trivial.
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