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Introduction to geometry
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ISBN: 0471504580 9780471504580 Year: 1980 Publisher: New York (N.Y.): Wiley

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Skew fields
Author:
ISBN: 1139883887 1107365910 1107370647 1107361001 110736812X 1299403727 1107363454 0511661908 9781107361003 0521272742 9780521272742 9780511661907 Year: 1983 Volume: 81 Publisher: Cambridge [Cambridgeshire] New York Cambridge University Press

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The book is written in three parts. Part I consists of preparatory work on algebras, needed in Parts II and III. This material is presented in a classical, though unusual, way. Part II consists of a modern description of the theory of Brauer groups over fields (from as elementary a point of view as possible). Part III covers some new developments in the theory which, until now, have not been available except in journals. The principal topic discussed in this section is reduced K,-theory. This book will be of interest to graduate students in pure mathematics and to professional mathematicians.

Theory of operator algebras I
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ISBN: 0387903917 3540903917 354042914X 3540429131 3642076882 3662104539 3642076890 3662104512 1461261902 1461261880 9783540429142 9783540429135 9780387903910 Year: 1979 Publisher: New York Heidelberg Berlin : Springer-Verlag,

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to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. A factor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.

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