El método no estandard en el estudio de la variedad de Leyes de álgebra de Lie

Abstract

This work synthesizes a number of articles about varieties of Lie algebras. The methods employed lie in the framework of nonstandard analysis. The notion of deformation for the variation of Lie algebra laws is replaced here by a perturbation satisfying a theorem of decomposition (Goze); this result provides a particular way of writing a point M near M0 with the help of infinitesimals. However, this formalism cannot describe such phenomena as the reducibility of the scheme structure defined by Jacobi’s rules. Then the authors show how their method operates to establish the rigidity of certain solvable Lie algebras (a law is rigid if its orbit under the canonical action of the full linear group is open). Note that most of the results of this paper can also be proved by canonical methods.