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Goze, Michel ; Ancochea Bermúdez , José María | Koninklijke Nederlandse Akademie van Wetenschappen | 1985The goal in this article is to give a constructive method describing the n-dimensional rigid Lie algebras ?, with "rigid'' meaning, in the simplest sense, that every Lie algebra law sufficiently close to ? is isomorphic to it. The authors use Li[...]texto impreso
Let Ln Kn3 be the affine variety of all n-dimensional Lie algebras over an algebraically closed field of characteristic zero. An element g 2 Ln can be identified with the bilinear mapping ? defining the multiplication in g. If f is an element o[...]texto impreso
Ancochea Bermúdez , José María ; Goze, Michel | Université de Paris VII, U.E.R. de Mathématiques | 1989An n -dimensional complex Lie algebra is rigid if its orbit under the canonical action of the full linear group is open in the variety defined by the Jacobi identities. The authors have perfected a method for obtaining solvable rigid Lie algebra[...]texto impreso
A Lie algebra g is called characteristically nilpotent if its algebra of derivations is nilpotent. The authors construct the examples of (2m+2)-dimensional characteristically nilpotent Lie algebras g2m+2 with characteristic sequence c(g2m+2) equ[...]texto impreso
A finite-dimensional complex Lie algebra g is characteristically nilpotent if its Lie algebra Derk(g) of derivations is nilpotent. Given two finite-dimensional nilpotent Lie algebras g1, g2, the authors construct a non-split central extension g1[...]texto impreso
In this work the authors classify the filiform Lie algebras (i.e., Lie algebras that are nilpotent with an adjoint derivation of maximal order) of dimension m=8 over the field of complex numbers. These algebras, introduced by M. Vergne in her t[...]texto impreso
Ancochea Bermúdez , José María ; Campoamor Stursberg, Otto Ruttwig | Int. Sci. Publ. Dr. Emil Minchev Totsuka machi | 2003We give examples of a family of nonsolvable complete Lie algebras isomorphic to the Lie algebra of derivations of a proper idealtexto impreso
Almaraz Luengo, Elena ; Ancochea Bermúdez , José María ; García Vergnolle, Lucía | Taylor & Francis | 2013-05It is proved that for any quasi-filiform of non-zero rank the solvable Lie algebra obtained by adjoining a maximal torus of outer derivations is complete. Further, for any positive integer m, it is shown that there exist solvable complete Lie a[...]texto impreso
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 sat[...]texto impreso
Lie algebra model theory studies the closure O() of the Gln(C)-orbit in the variety Ln of Lie algebra laws of a law on Cn using nonstandard analysis. In this context, given a Lie algebra law , a contraction of is a law ? with ? 2 O(). On the o[...]texto impreso
We compute the ?rst and second cohomology groups with coe?cients in the adjoint module of frobeniusian model algebras whose parameters move in a dense open subset of C p?1, and obtain upper bounds for the dimension of cohomology groups of froben[...]texto impreso
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 crite[...]texto impreso
In this paper we prove that in N9, the variety of complex nilpotent Lie algebras of dimension 9, there exists a unique irreducible component intersecting the open subset of all filiform Lie algebras of dimension 9. It is also proved that, unlike[...]texto impreso
We present the classification of naturally graded nilpotent Lie algebras g with linear characteristic sequence in arbitrary dimension modulo a finite set of particular solutions corresponding to solutions with very small nilindex with respect to[...]texto impreso
Ancochea Bermúdez , José María ; Margalef Bentabol, Juan ; Sánchez Hernández, Jonathan | Heldermann | 2007Dans cette note, en utilisant les notions de déformation et contraction des lois d'algèbres de Lie et Leibniz, on montre que les variétés algébriques des lois d'algèbres de Leibniz complexes et de Leibniz nilpotentes de dimension supérieure ou é[...]
