Información del autor
Autor Ancochea Bermúdez, José María |
Documentos disponibles escritos por este autor (39)
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Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; García Vergnolle, Lucía ; Goze, M. | Springer | 2007We present all real solvable algebraically rigid Lie algebras of dimension lower or equal than eight. We point out the differences that distinguish the real and complex classification of solvable rigid Lie algebrastexto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; García Vergnolle, Lucía | Elsevier Science | 2006On montre qu’une algèbre de Lie résoluble rigide réelle n’est pas nécessairement complètement résoluble. On construit un exemple n ? t de dimension minimale dont le tore extérieur t n’est pas formé par des dérivations ad-semi-simples surR. Nous [...]texto impreso
In this article the authors study filiform nilpotent Lie algebras n which possess a given torus T of semisimple derivations. The solvable Lie algebras obtained by a semidirect product T?n depend, up to isomorphism, on one or many parameters (con[...]texto impreso
We show the rigidity of a parameterized family of solvable Leibniz non-Lie algebras in arbitrary dimension, obtaining an irreducible component in the variety L epsilon(n) that does not intersect the variety of Lie algebras non-trivially. Moreove[...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; Gonzalez-Gascon, F. | Elsevier | 2003We show that analytic R-3 vector fields having the property of being transversal to either analytic functions or foliations F-2, or parallel. to a foliation, are free from ergodicity and turbulence. The absence of turbulence and ergodicity via i[...]texto impreso
Jacobson’s theorem says that if a finite-dimensiona complex Lie algebra L has a nondegenerate derivation, then L is nilpotent. The converse to this theorem is false. That is, there are nilpotent Lie algebras all of whose derivations are nilpoten[...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig | Universidad de Extremadura, Departamento de Matemáticas | 2001Jacobson proved in 1955 that any Lie algebra over a field of characteristic zero which has nondegenerate derivations is nilpotent. Dixmier and Lister proved in 1957 that the converse is false. They provided an example of a new class of Lie algeb[...]texto impreso
The authors give a complete list of the 7-dimensional complex nilpotent Lie algebras. This classification is obtained by using an invariant of nilpotent Lie algebras, called a characteristic sequence and defined by the maximum of the Segre symbo[...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; García Vergnolle, Lucía | Elsevier | 2011The whole class of complex Lie algebras g having a naturally graded nilradical with characteristic sequence c(g) = (dim g ? 2, 1, 1) is classified. It is shown that up to one exception, such Lie algebras are solvable.texto impreso
In this paper we consider the problem of classifying the (n ? 5)-filiform Lie algebras. This is the first index for which infinite parametrized families appear, as can be seen in dimension 7. Moreover we obtain large families of characteristic n[...]texto impreso
The complete classification of real solvable rigid Lie algebras possessing a nilradical of dimension at most six is given. Eleven new isomorphism classes of indecomposable algebras are obtained. It is further shown that the resulting solvable Li[...]texto impreso
It is shown that for a finite-dimensional solvable rigid Lie algebra r, its rank is upper bounded by the length of the characteristic sequence c(n) of its nilradical n. For any characteristic sequence c = (n(1),..., n(k,) 1), it is proved that t[...]texto impreso
We determine the solvable complete Lie algebras whose nilradical is isomorphic to a filiform Lie algebra. Moreover we show that for any positive integer n there exists a solvable complete Lie algebra whose second cohomology group with values in [...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; García Vergnolle, Lucía ; Sánchez Hernández, J. | Academic Press | 2008-03-15On détermine les classes d’isomorphisme des algèbres de Jordan en dimension deux sur le corps des nombres réels. En utilisant des techniques d’Analyse Non Standard, on étudie les propriétés de la variét des lois d’algèbres de Jordan, et aussi le[...]texto impreso
In this article, we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformat[...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; García Vergnolle, Lucía | Hikari | 2006Let g = s n r be an indecomposable Lie algebra with nontrivial semisimple Levi subalgebra s and nontrivial solvable radical r. In this note it is proved that r cannot be isomorphic to a filiform nilpotent Lie algebra. The proof uses the fact tha[...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; García Vergnolle, Lucía | UCM | 2012For the only quasi-filiform Lie algebra L5,3 admitting a Levi factor in its Lie algebra of derivations, the extensions by derivations are classified over C and R. Moreover, the invariants of these extensions are computed.texto impreso
One of the main achievements of the paper under review is the construction of new classes of characteristically nilpotent Lie algebras that are not filiform. In fact, in Theorem 4.5 one describes, for arbitrary m 4, a characteristically nilpote[...]texto impreso
We classify the (n ? 5)-filiform Lie algebras which have the additional property of a non-abelian derived subalgebra. Moreover we show that if a (n ? 5)-filiform Lie algebra is characteristically nilpotent, then it must be 2-abelian.texto impreso
In this work large families of naturally graded nilpotent Lie algebras in arbitrary dimension and characteristic sequence (n; q; 1) with n ? 1(mod 2) satisfying the centralizer property are given. This centralizer property constitutes a generali[...]texto impreso
We construct large families of characteristically nilpotent Lie algebras by analyzing the centralizers of the ideals in the central descending sequence of the Lie algebraQn and deforming its extensions preserving the structure of these centraliz[...]texto impreso
We show that the only indecomposable solvable Leibniz non-Lie algebra L0 with nilradical of maximal nilpotence index is rigid in any dimension, andmoreover that it is complete, i.e., only possesses inner derivations. The possible contractions of[...]texto impreso
We prove first that every (n ? p)-filiform Lie algebra, p ? 3, is the nilradical of a solvable, nonnilpotent rigid Lie algebra. We also analize howthis result extends to (n ? 4)-filiform Lie algebras. For this purpose, we give a classificaction [...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig | Universidad Complutense de Madrid | 2002In [6] and [7] the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie al[...]texto impreso
After having given the classification of solvable rigid Lie algebras of low dimensions, we study the general case concerning rigid Lie algebras whose nilradical is filiform and present their classification.texto impreso
In his thesis, Carles made the following conjecture: Every rigid Lie algebra is defined on the field Q. This was quite an interesting question because a positive answer would give a nice explanation of the fact that simple Lie algebras are defin[...]texto impreso
We show that the product by generators preserves the characteristic nilpotence of Lie algebras, provided that the multiplied algebras belongs to the class of S-algebras. In particular, this shows the existence of nonsplit characteristically nilp[...]texto impreso
Let Nn be the variety of n-dimensional complex nilpotent Lie algebras. We know that this algebraic variety is reducible for n?11 and irreducible for n?6. In this work we prove that N7 is composed of two algebraic components and that N8 is also r[...]texto impreso
This paper consists of a description of the variety of two dimensional associative algebras within the framework of Nonstandard Analysis. By decomposing each algebra in A2 as sum of a Jordan algebra and a Lie algebra, we calculate th isomorphism[...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; Goze, M. | Elsevier | 2003-12-15Dans la variété des algèbres de Lie nilpotentes de dimension finie sur le corps des nombres complexes, l'ensemble des algèbres de Lie caractéristiquement nilpotentes n'est pas fermé. Nous montrons dans cette Note qu'il n'est pas ouvert non plus.texto impreso
One knows that a solvable rigid Lie algebra is algebraic and can be written as a semidirect product of the form g=T?n if n is the maximal nilpotent ideal and T a torus on n . The main result of the paper is equivalent to the following: If g [...]texto impreso
It is shown that the two-known series of rank one (Formula presented.) and rank two (Formula presented.) finite-dimensional solvable rigid Lie algebras with non-vanishing second cohomology can be extended to solvable rigid Lie algebras of arbitr[...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; Vergnolle, L.G. | IOP science | 2006The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analysed, and their generalized Casimir invariants are calculated. It is shown that rank one solvable algebras[...]texto impreso
The authors give an approach to the classification of 7-dimensional nilpotent algebras. They illustrate the use of the invariant of nilpotent Lie algebras, called characteristic sequence, and defined by the maximum of the ordered sequences of th[...]texto impreso
Ancochea Bermúdez, José María ; Gómez-Martín, José Ramón ; Valeiras, Gerardo ; Goze, Michel | Elsevier Science | 1996-01-15In this paper we determine all the components fo the variety of complex nilpotent Lie algebras of dimension 8. The technique is similar to that used for the smaller dimensions. But in this case big difficulties appear resulting from the complexi[...]texto impreso
The scheme of the Lie algebras of dimension n is reducible for n?2 and the number of its components is bounded asymptotically by exp(n/4) . The same problem is studied by the authors for the subvariety N n of the nilpotent Lie algebras of di[...]texto impreso
Let Nn be the variety of nilpotent Lie algebra laws of a given complex vector space Cn. M. Vergne showed ["Variété des algèbres de Lie nilpotentes'', Thèse de 3ème cycle, Spéc. Math., Paris, 1966; BullSig(110) 1967:299; Bull. Soc. Math. France 9[...]texto impreso
We introduce the product by generators of two nilpotent Lie algebras as a central extension of the direct sum and analyze symplectic structures on them. We show that, up to few exceptions, these products do not admit symplectic forms. Besides a [...]texto impreso
In this paper the authors propose a new approach to the study of weight systems. Instead of considering graphs whose vertices correspond to the generators of a Lie algebra (as for Cartan subalgebras in the semisimple case), the authors consider [...]