Algebra and Operator Theory: Proceedings of the Colloquium by Sh. A. Ayupov, B. A. Omirov (auth.), Yusupdjan Khakimdjanov, PDF

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

ISBN-10: 9401061300

ISBN-13: 9789401061308

ISBN-10: 9401150729

ISBN-13: 9789401150729

This quantity offers the lectures given in the course of 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 subject matters mentioned listed here are deformation of Lie algebras, cohomology thought, 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, reminiscent of supermanifolds. The papers on operator thought care for the learn of specific sorts of operator algebras. This quantity additionally encompasses a designated creation to the speculation of quantum teams.
Audience: This booklet is meant for graduate scholars specialising in algebra, differential geometry, operator concept, and theoretical physics, and for researchers in arithmetic and theoretical physics.

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2 Lorsqu'on represente les singularites de Klein comme les varietes quotients du plan affine par l'action d'un sous-groupe fini de 8L(2), ces surfaces heritent d'une structure de Poisson provenant de la structure symplectique du plan. Comme par ailleurs, un sous-groupe fini G de 8L(2) opere dans l'algebre de Weyl AI(C) par automorphismes, l'algebre des invariants Al (C)G est une deformation de la surface de Klein correspondante. Nous montrons que la filtration de Bernstein de Al (C) induit naturellement une filtration sur Ie groupe H Ho(A I (C)G) dont Ie gradue associe est isomorphe it.

Xn ) is a basis of L n (the undefined brackets being zero excepted the brackets obtained by antisymmetry). This is, in a certain manner, the simplest filiform Lie algebra. 2. Let n = 2k + 1 be an odd integer and let Qn be the (n Lie algebra defined in the basis (Xo, Xl, ... ,Xn ) by [XO, X;] = Xi+1, i = [Xi, X n - i ] = (_l)i X n , + I)-dimensional 1, ... , n - 1; i = 1, ... , k. This is a filiform Lie algebra. In the basis (Zo, Zl, ... ,Zn), where Zo = Xo + Xl, Zi = Xi, i =, ... ,n, this Lie algebra is defined by [ZO, Zi] = Zi+ll [Zi, Zn-i] i = 1, ...

13] M. <;, 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.

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Algebra and Operator Theory: Proceedings of the Colloquium in Tashkent, 1997 by Sh. A. Ayupov, B. A. Omirov (auth.), Yusupdjan Khakimdjanov, Michel Goze, Shavkat A. Ayupov (eds.)


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