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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 | 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.![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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.