Algebra and Operator Theory, 1998
Proceedings of the Colloquium in Tashkent, 1997

This volume presents the lectures given during the second French-Uzbek Colloquium on Algebra and Operator Theory which took place in Tashkent in 1997, at the Mathematical Institute of the Uzbekistan Academy of Sciences. Among the algebraic topics discussed here are deformation of Lie algebras, cohomology theory, the algebraic variety of the laws of Lie algebras, Euler equations on Lie algebras, Leibniz algebras, and real K-theory. Some contributions have a geometrical aspect, such as supermanifolds. The papers on operator theory deal with the study of certain types of operator algebras. This volume also contains a detailed introduction to the theory of quantum groups.
Audience: This book is intended for graduate students specialising in algebra, differential geometry, operator theory, and theoretical physics, and for researchers in mathematics and theoretical physics.

Preface. On Leibniz Algebras; Sh.A. Ayupov, B.A. Omirov. A Moduli Problem Related to Complex Supermanifolds; A.L. Onishchik. Comparaison de l'homologie de Hochschild et de l'homologie de Poisson pour une déformation des surfaces de Klein; J. Alev, T. Lambre. Quelques résultats en K-Théorie réelle; C.N. Costinescu. Some Nilpotent Lie Algebras and their Applications; M. Goze, Yu. Khakimdjanov. Algèbres de Lie rigides; M. Goze, J.M. Ancochea Bermudez. Family of p-Filiform Lie Algebras; J.M. Cabezas, et al. The Functional Representation of Commutative Symmetric Operator Algebras in Pontryagin Space; V.I. Chilin, S.Sh. Masharipova. Continuous Decomposition of Real Von Neumann Algebras of Type III; Sh. Usmanov. Espaces vectoriels différentiels; K. Khakimdjanova. Complétude de l'équation d'Euler; Sh. Bromberg, A. Medina. On Invariants of Second Order Linear Partial Differential Equations in Two Variables; U. Bekbaev. Lattice-Ordered Groupoids and their Prime Spectrums; Dj. Khadjiev, T.M. Shamilev. Sur un problème d'Elie Cartan; Th. Hangan. Classification of Non-Commutative Arens Algebras Associated with Semi-Finite Traces; R.Z. Abdullaev. Order Unit Space of Type In with Banach Ball Property; M.A. Berdikulov. On Markov Random Fields on UHF Algebras; N.N. Ganikhodzhaev, F.M. Mukhamedov. Injectivity, Amenability, Semi Discreteness and Hyperfiniteness in Real W*-Algebras; A. Rakhimov, B. Boykabilov. Contractive Projections on Facially Symmetric Spaces; N.J. Yadgorov, M.M. Ibragimov. The Property (talpha) for Locally Compact Connected Groups; K.K. Muminov. Grupos Cuánticos; Ch. Kassel. On the Group of Weak Automorphisms of a Family of Equivalence Relations; Th. Gschwend, O.H.Kegel. Index.