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Autor Ancochea Bermúdez, José María |
Documentos disponibles escritos por este autor (39)
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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.![]()
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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 [...]