The theory of operator algebras acting on a Hilbert space was initiated in thirties by papers of Murray and von Neumann. In these papers they have studied the structure of algebras which later were called von Neu mann algebras or W* -algebras. They are weakly closed complex *-algebras of operators on a Hilbert space. At present the theory of von Neumann algebras is a deeply developed theory with various applications. In the framework of von Neumann algebras theory the study of fac tors (i.e. W* -algebras with trivial centres) is very important, since they are comparatively simple and...

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...

The monograph is devoted to the real counterpart of the theory of operator algebras, namely to the theory of real W*-algebras. We develop a real analogue of index theory for subfactors of W*- factors and study actions of various kinds of groups (finite, discrete, amenable, abelian, compact) on different types of real W*-algebras. An abstract (non spatial) generalization of real W*-algebra - so called real AW*-algebras are also investigated. These algebras present a real counterpart of Kaplansky algebras - complex AW*-algebras. Type decomposition for real AW*-algebras is obtained and ...