Publication:
Le rang du systeme linéaire des racines d'une algèbre de Lie rigide résoluble complexe

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Publication Date
1992
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Taylor & Francis
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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 is rigid then T is a maximal torus on n . The authors then study algebras of this form where n is a filiform nilpotent algebra. A classification of this law is given in the case in which the weights of T are kα , with 1≤k≤n=dimn .
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BRATZLAVSKY F. Sur les algèbres admettent un tore d'autornorphismes donne. J. Algebra 30, 305-316 (19741. CARLES R. Sur la structure des algèbres de Lie rigides. Ann. Inst. Fourier 34, 65-82 (1984). CARLES R. Sur certaines classes d'algèbres de Lie rigides . Math Ann 272; 477-488 (1985) FAVRE G. Système de poids sur une algèbre de Lie nilpotente. Manuscripts Math. 9. 53-90 (19731. GOZE M. ANCOCHEA BERMUDEZ J. M. Algèbres de Lie rigides. Indagationes Math 88. 397-415 (1985). GOZE M. ANCOCHEA BERMUDEZ J.M. Algèbres de Lie rigides dont le nilradical est filiforme. C.R. A.Sc. Paris t. 312 . 21-24 (1991). VERGNE M. Cohomologie des algèbres de Lie nllpotentes. Applications B l'etude de la variété des algèbres de Lie nilpotentes. Bull. Soc. Math. France 98, 81-116 (1970).
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