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

This quantity provides the lectures given through the moment French-Uzbek Colloquium on Algebra and Operator thought which came about in Tashkent in 1997, on the Mathematical Institute of the Uzbekistan Academy of Sciences. one of the algebraic themes mentioned listed below 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 point, corresponding to supermanifolds. The papers on operator idea take care of the research of particular types of operator algebras. This quantity additionally features a special creation to the speculation of quantum teams. *Audience:* This ebook is meant for graduate scholars specialising in algebra, differential geometry, operator thought, and theoretical physics, and for researchers in arithmetic and theoretical physics.

**Read Online or Download Algebra and Operator Theory: Proceedings of the Colloquium in Tashkent, 1997 PDF**

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**Additional info for Algebra and Operator Theory: Proceedings of the Colloquium in Tashkent, 1997**

**Sample text**

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.