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E {C[X b X 2, X 3], C[X1, X 2, X 3]} + (F), (17) pour tous nbn2,n3 E N et i = 1,2,3. Les for mules (13) montrent que Ie seul cas a etudier est Ie "cas type" Xfl X~2 Xf3 F{, avec nl -=1= O. L'equation (15) implique d'abord nlXfl X~2 Xf3 F{ +n2X~1-IX~2+1 Xf3 F~ = Xfl X:;2 Xf3(nl + n3Xfl-1X~2 Xf3+ 1F~ + n2 + n3)F. Puis, par derivation on a {X 2, Xfl X~2 Xf3+ 1} = (n3 + l)Xfl X~2 Xf3 F{ - nlXf1-1 X~2 Xf3+ 1F~ (18) et {Xfl X:;2+ 1 Xf3 ,X3} = (n2+ I)Xfl X:;2 Xf3 F{ -nlXf1-1 X:;2+ 1 Xf3 F~. 2), (18) et (19) constituent un systeme lineaire en les inconnues 1X"'3 p,' X"'l 1 -1 X"'2+ 23 2 1F' X"'1-1 X"'2 X"'3+ 1 2 3 3 de determinant -n1 (n3 (n3 + 1) + n2 (0:2 + 1) + n1 0:1), entier strictement negatif.

Journal of Pure and Applied Algebra, 72, 1991,95-108. [14] M. , 54, 1987, 641-647. S. : 13A50, 13DlO, 16E40. COSTINESCU Departement de Mathematiques, Universite Technique de Constructions, Bucarest, RO UMANIE Abstract. On etudie la suite spectrale d'Atiyah-Hirzebruch associee a KO* (HS(n,k)), ou HS(n,k) designe la variete quatemionique de Stiefel. Les isomorphismes de groupes abeliens : KO*(HS(n,k)) ~E 2 (HS(n,k))~ E~(HS(n,k)) qui ont ete etablis,donnent la structure Zs- graduee de la K- theorie reelle.

This set is endowed of a structure of algebraic variety. l is the bracket of the given Lie algebra. l) where the last law is defined by en. l). The topological notions are related with the Zariski topology. l) is Zariski open on Ln. Let us consider the ring C[Cjk] of polynomials of (n 3 -n 2 )j2 formal variables Cjk (Cjk = -Ckj) and denote by J the ideal of C[Cjk] generated by the Jacobi polynomials.

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