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5] J. Dixmier, Sur les algebres de Weyl, Bull. Soc. Math. Prance, 96, 1968. [6] A. Guichardet, Homologie de Hochschild des deformations d'algebres de polynomes, a paraitre. [7] C. Kassel, L'homologie cyclique des algebres enveloppantes, Invent. , 91, 1988, 221-251. [8] M. Lorenz, Crossed Products: Characters, Cyclic Homology, and Grothendieck Groups, Non commutative Rings, Math. Sciences Research Institute Publications, 24, Springer Verlag, 1992, 69-98. [9] S. , 818, Springer Verlag, 1980. [10] P.

Let 9 be a filiform Lie algebra of dimension n + 1 2 7 nonisomorphic to £n and Qn- Then 9 is characteristically nilpotent if and only if 9 is not isomorphic to its sill algebra . 2 Description of Lie algebras whose nilradical is filiform Let 9 be a Lie algebra. The semidirect decomposition 9 = s EI1 r holds, where r is the radical in 9 (the Levi decomposition), and all Levi subalgebras are mutually conjugate (Mal'tsev's theorem [10]). These theorems suggest to consider the problem of classification of Lie algebras with a fixed radical [15].

Dans ce qui suit nous nous placerons sous l'hypothese de la derniere proposition; rappelons maintenant un theoreme de structure (voir [12]) bien adapte a la K-theorie reelle. 2 Supposons que Tors (K*(X)) = a et que la conjugaison decompose Ie groupe abelien (K* (X) sous la forme: (K*(X) = M+ EBTEBT* de sorte que soit la multiplication par+1 (respectivement-1) sur M+(respectivement sur M _) et d 'autre part echange T et T*; en outre soient hI, ... , h n E KO* (X) tels que les c(h i ) forment une base pour K* (+) ® (M+ EB M_) en tant que K* (+) -module.

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