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Author: Donald S. Passman
Publisher: Courier Corporation
ISBN: 0486497402
Category : Mathematics
Languages : en
Pages : 484
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Book Description
"This groundbreaking monograph in advanced algebra addresses crossed products, which involve group and ring theory. According to the author's Preface,crossed products have advanced from their first occurrence in finite dimensional division algebras and central simple algebras to a closer relationship with the study of infinite group algebras, group-graded rings, and the Galois theory of noncommutative rings. 1989 edition"--
Author: Donald S. Passman
Publisher: Courier Corporation
ISBN: 0486497402
Category : Mathematics
Languages : en
Pages : 484
Get Book
Book Description
"This groundbreaking monograph in advanced algebra addresses crossed products, which involve group and ring theory. According to the author's Preface,crossed products have advanced from their first occurrence in finite dimensional division algebras and central simple algebras to a closer relationship with the study of infinite group algebras, group-graded rings, and the Galois theory of noncommutative rings. 1989 edition"--
Author: Donald S. Passman
Publisher:
ISBN:
Category : MATHEMATICS
Languages : en
Pages :
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Book Description
"This groundbreaking monograph in advanced algebra addresses crossed products, which involve group and ring theory. According to the author's Preface, crossed products have advanced from their first occurrence in finite dimensional division algebras and central simple algebras to a closer relationship with the study of infinite group algebras, group-graded rings, and the Galois theory of noncommutative rings. 1989 edition"--.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 128
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Book Description
Author: Thierry Giordano
Publisher: Springer
ISBN: 3319708694
Category : Mathematics
Languages : en
Pages : 498
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Book Description
This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures. The first one, given by Andrew Toms, presents the basic properties of the Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an introduction to group actions on C*-algebras and their crossed products, with emphasis on the simple case and when the crossed products are classifiable. The third one, given by David Kerr, treats various developments related to measure-theoretic and topological aspects of crossed products, focusing on internal and external approximation concepts, both for groups and C*-algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the theory of topological orbit equivalence, with particular attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.
Author: G. Karpilovsky
Publisher: Elsevier
ISBN: 9780080872537
Category : Mathematics
Languages : en
Pages : 347
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Book Description
In the past 15 years, the theory of crossed products has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings. The purpose of this monograph is to give, in a self-contained manner, an up-to-date account of various aspects of this development, in an effort to convey a comprehensive picture of the current state of the subject. It is assumed that the reader has had the equivalent of a standard first-year graduate course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, which briefly surveys topics required later in the book.
Author: M. Rordam
Publisher: Springer Science & Business Media
ISBN: 3662048256
Category : Mathematics
Languages : en
Pages : 206
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Book Description
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. Afactor 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.
Author: Dana P. Williams
Publisher: American Mathematical Soc.
ISBN: 0821842420
Category : Mathematics
Languages : en
Pages : 528
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Book Description
The theory of crossed products is extremely rich and intriguing. There are applications not only to operator algebras, but to subjects as varied as noncommutative geometry and mathematical physics. This book provides a detailed introduction to this vast subject suitable for graduate students and others whose research has contact with crossed product $C*$-algebras. In addition to providing the basic definitions and results, the main focus of this book is the fine ideal structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. In particular, there is an in-depth analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Morita equivalence of $C*$-algebras are based. There is also a detailed treatment of the generalized Effros-Hahn conjecture and its proof due to Gootman, Rosenberg, and Sauvageot. This book is meant to be self-contained and accessible to any graduate student coming out of a first course on operator algebras. There are appendices that deal with ancillary subjects, which while not central to the subject, are nevertheless crucial for a complete understanding of the material. Some of the appendices will be of independent interest. To view another book by this author, please visit Morita Equivalence and Continuous-Trace $C*$-Algebras.
Author: Donald S. Passman
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 84
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Book Description
For readers with a basic graduate level background in algebra, these ten articles provide a readable introduction to three major interrelated subjects of noncommutative algebra. The theme is the interplay between group theory and ring theory, dealing specifically with group rings, crossed products, and the Galois theory of rings. The author has carefully included most definitions, to keep the required background minimal. Furthermore, each article contains a selection of results on the given topic, a limited number of proofs or sketches, and at least a few open problems.
Author: Peter A. Fillmore
Publisher: American Mathematical Soc.
ISBN: 9780821871218
Category : Mathematics
Languages : en
Pages : 338
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Book Description
The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas - both within and outside mathematics. The field was a natural candidate for a 1994-1995 program year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences. This volume contains a selection of papers that arose from the seminars and workshops of the program. Topics covered include the classification of amenable C*-algebras, the Baum-Connes conjecture, E[subscript 0] semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: Can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?
Author: Surender K Jain
Publisher: World Scientific
ISBN: 9814553123
Category :
Languages : en
Pages : 394
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Book Description
This volume consists of a collection of invited papers on the theory of rings and modules, most of which were presented at the biennial Ohio State — Denison Conference, May 1992, in memory of Hans Zassenhaus. The topics of these papers represent many modern trends in Ring Theory. The wide variety of methodologies and techniques demonstrated will be valuable in particular to young researchers in the area. Covering a broad range, this book should appeal to a wide spectrum of researchers in algebra and number theory.
