By Sh. A. Ayupov, B. A. Omirov (auth.), Yusupdjan Khakimdjanov, Michel Goze, Shavkat A. Ayupov (eds.)

This quantity offers the lectures given in the course of the moment French-Uzbek Colloquium on Algebra and Operator idea which happened in Tashkent in 1997, on the Mathematical Institute of the Uzbekistan Academy of Sciences. one of the algebraic themes mentioned listed here are deformation of Lie algebras, cohomology concept, the algebraic number of the legislation of Lie algebras, Euler equations on Lie algebras, Leibniz algebras, and genuine *K*-theory. a few contributions have a geometric element, akin to supermanifolds. The papers on operator thought care for the examine of particular types of operator algebras. This quantity additionally features a unique advent to the speculation of quantum teams. *Audience:* This e-book is meant for graduate scholars specialising in algebra, differential geometry, operator thought, and theoretical physics, and for researchers in arithmetic and theoretical physics.

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Math. , 95(1985), 255-260. ru COMPARAISON DE L'HOMOLOGIE DE HOCHSCHILD ET DE L'HOMOLOGIE DE POISSON POUR UNE DEFORMATION DES SURFACES DE KLEIN J. ALEV, T. A. P. 1039, 51687 Reims Cedex, Prance. A. , 91405 Orsay Cedex, Prance. Abstract. Let p G be the quotient variety of the affine plane by the action of a finite group G C 8L(2, C); then pG inherits in a natural way a Poisson algebra structure. Let Al (C) be the first Weyl algebra C[p, qJ with the relation pq- qp = 1, on which G acts by automorphisrns in such a way that the invariant algebra Al (C)G is a deformation of pG.

Tenant compte de la definition de Pn il resulte que toute M E Sp(n) C U(2n) est une isometrie de H', c'est-a-dire: M J = J M; on en doouit que la multiplication par M definit un H-automorphisme de E (muni de sa structure quaternionique). 6. est ainsi achevee. 5. \n(Pn)] s'identifie comme Z- algebre suplimentee a la Z algebre Z[7rl"" , 7rn ] et de plus les elements 7ri(Pn) avec n = k + 1 ~ i ~ n appartiennent a P (voir [UD. 1. ( ROUX ) En tant qu'algebre Zz-graduee, K*(HS(n, k)) est isamarphe a l'algebre exterieure AZ [7rn -k+l,'" ,7rn ], au chaque 7ri est de degre -l.

1, l'homomorphisme de complexification c : kOn(SO) -> kn(SO) est un isomorphisme pour n == 0 (modulo8) et il est un monomorphisme pour n == 4 (modulo 8). Rappelons aussi que l'on a I'isomorphisme: ch : K*(X) 0Q -> H*(X; Q) ou ch designe Ie caractere de Chern (voir [2]). 3. 1. sous la forme suivante: ou Ez et E oo designent les termes de la suite spectrale generalisee, associee a h(X). II en r€sulte que pour tout s ~ 2 les differentielles d s prennent leurs valeurs dans Ie sous-groupe de torsion du terme E s ; on obtient pour tout s ~ 2 les epimOl1)hismes canoniques: H*(TorsEs ) -> Tors(H* E s ~ E s + 1 ) Partie 2 Le but est la demonstration d'un resultat connu de LAZAROV (voir [9]): la Z- algebre Zs -graduee J