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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 algebras![]()
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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.![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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.![]()
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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[...]![]()
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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.![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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.