The Algebraic Structure Of Crossed Products

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The Algebraic Structure of Crossed Products

Author : G. Karpilovsky
Publisher : Elsevier
ISBN 13 : 9780080872537
Total Pages : 347 pages
Book Rating : 4.8/5 (725 download)

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Book Synopsis The Algebraic Structure of Crossed Products by : G. Karpilovsky

Download or read book The Algebraic Structure of Crossed Products written by G. Karpilovsky and published by Elsevier. This book was released on 1987-05-01 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Crossed Products of $C^*$-Algebras

Author : Dana P. Williams
Publisher : American Mathematical Soc.
ISBN 13 : 0821842420
Total Pages : 546 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Crossed Products of $C^*$-Algebras by : Dana P. Williams

Download or read book Crossed Products of $C^*$-Algebras written by Dana P. Williams and published by American Mathematical Soc.. This book was released on 2007 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Structure of Algebras

Author : Abraham Adrian Albert
Publisher : American Mathematical Soc.
ISBN 13 : 0821810243
Total Pages : 224 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Structure of Algebras by : Abraham Adrian Albert

Download or read book Structure of Algebras written by Abraham Adrian Albert and published by American Mathematical Soc.. This book was released on 1939-12-31 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI consists of the study of the abelian group of cyclic systems which is applied in Chapter VII to yield the theory of the structure of direct products of cyclic algebras and the consequent properties of norms in cyclic fields. This chapter is closed with the theory of $p$-algebras. In Chapter VIII an exposition is given of the theory of the representations of algebras. The treatment is somewhat novel in that while the recent expositions have used representation theorems to obtain a number of results on algebras, here the theorems on algebras are themselves used in the derivation of results on representations. The presentation has its inspiration in the author's work on the theory of Riemann matrices and is concluded by the introduction to the generalization (by H. Weyl and the author) of that theory. The theory of involutorial simple algebras is derived in Chapter X both for algebras over general fields and over the rational field. The results are also applied in the determination of the structure of the multiplication algebras of all generalized Riemann matrices, a result which is seen in Chapter XI to imply a complete solution of the principal problem on Riemann matrices.

Crossed Products of C*-Algebras, Topological Dynamics, and Classification

Author : Thierry Giordano
Publisher : Springer
ISBN 13 : 3319708694
Total Pages : 498 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Crossed Products of C*-Algebras, Topological Dynamics, and Classification by : Thierry Giordano

Download or read book Crossed Products of C*-Algebras, Topological Dynamics, and Classification written by Thierry Giordano and published by Springer. This book was released on 2018-08-28 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension

Author : Aidan Sims
Publisher : Springer Nature
ISBN 13 : 3030397130
Total Pages : 163 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension by : Aidan Sims

Download or read book Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension written by Aidan Sims and published by Springer Nature. This book was released on 2020-06-22 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the notes of the lectures given at the Advanced Course on Crossed Products, Groupoids, and Rokhlin dimension, that took place at the Centre de Recerca Matemàtica (CRM) from March 13 to March 17, 2017. The notes consist of three series of lectures. The first one was given by Dana Williams (Dartmouth College), and served as an introduction to crossed products of C*-algebras and the study of their structure. The second series of lectures was delivered by Aidan Sims (Wollongong), who gave an overview of the theory of topological groupoids (as a model for groups and group actions) and groupoid C*-algebras, with particular emphasis on the case of étale groupoids. Finally, the last series was delivered by Gábor Szabó (Copenhagen), and consisted of an introduction to Rokhlin type properties (mostly centered around the work of Hirshberg, Winter and Zacharias) with hints to the more advanced theory related to groupoids.

The Algebraic Structure of Group Rings

Author : Donald S. Passman
Publisher : Courier Corporation
ISBN 13 : 0486482065
Total Pages : 754 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis The Algebraic Structure of Group Rings by : Donald S. Passman

Download or read book The Algebraic Structure of Group Rings written by Donald S. Passman and published by Courier Corporation. This book was released on 2011-01-01 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: "'Highly recommended' by the Bulletin of the London Mathematical Society, this book offers a comprehensive, self-contained treatment of group rings. The subject involves the intersection of two essentially different disciplines, group theory and ring theory. The Bulletin of the American Mathematical Society hailed this treatment as 'a majestic account,' proclaiming it "encyclopedic and lucid." 1985 edition"--

Crossed Products of Operator Algebras

Author : Elias G. Katsoulis
Publisher : American Mathematical Soc.
ISBN 13 : 1470435454
Total Pages : 85 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Crossed Products of Operator Algebras by : Elias G. Katsoulis

Download or read book Crossed Products of Operator Algebras written by Elias G. Katsoulis and published by American Mathematical Soc.. This book was released on 2019-04-10 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.

Algebraic Structures and Applications

Author : Sergei Silvestrov
Publisher : Springer Nature
ISBN 13 : 3030418502
Total Pages : 976 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Algebraic Structures and Applications by : Sergei Silvestrov

Download or read book Algebraic Structures and Applications written by Sergei Silvestrov and published by Springer Nature. This book was released on 2020-06-18 with total page 976 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics. The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas.

Group Rings, Crossed Products, and Galois Theory

Author : Donald S. Passman
Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Group Rings, Crossed Products, and Galois Theory by : Donald S. Passman

Download or read book Group Rings, Crossed Products, and Galois Theory written by Donald S. Passman and published by . This book was released on 1986 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Structure of Algebras

Author : A. A. Albert
Publisher : American Mathematical Soc.
ISBN 13 : 0821874608
Total Pages : 224 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Structure of Algebras by : A. A. Albert

Download or read book Structure of Algebras written by A. A. Albert and published by American Mathematical Soc.. This book was released on 1964 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Continuous Crossed Products and Type III Von Neumann Algebras

Author : Alfons van Daele
Publisher : Cambridge University Press
ISBN 13 : 0521219752
Total Pages : 81 pages
Book Rating : 4.5/5 (212 download)

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Book Synopsis Continuous Crossed Products and Type III Von Neumann Algebras by : Alfons van Daele

Download or read book Continuous Crossed Products and Type III Von Neumann Algebras written by Alfons van Daele and published by Cambridge University Press. This book was released on 1978-07-20 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the theory of von Neumann algebras.

Infinite Crossed Products

Author : Donald S. Passman
Publisher : Courier Corporation
ISBN 13 : 0486315940
Total Pages : 484 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Infinite Crossed Products by : Donald S. Passman

Download or read book Infinite Crossed Products written by Donald S. Passman and published by Courier Corporation. This book was released on 2013-07-24 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This groundbreaking monograph in advanced algebra addresses crossed products, which involve group and ring theory and the study of infinite group algebras, group-graded rings, and the Galois theory of noncommutative rings. 1989 edition.

An Introduction to C*-Algebras and the Classification Program

Author : Karen R. Strung
Publisher : Springer Nature
ISBN 13 : 3030474658
Total Pages : 322 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis An Introduction to C*-Algebras and the Classification Program by : Karen R. Strung

Download or read book An Introduction to C*-Algebras and the Classification Program written by Karen R. Strung and published by Springer Nature. This book was released on 2020-12-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further.

Infinite Crossed Products

Author : Donald S. Passman
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (97 download)

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Book Synopsis Infinite Crossed Products by : Donald S. Passman

Download or read book Infinite Crossed Products written by Donald S. Passman and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--.

Crossed Products with Continuous Trace

Author : Siegfried Echterhoff
Publisher : American Mathematical Soc.
ISBN 13 : 0821805630
Total Pages : 149 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Crossed Products with Continuous Trace by : Siegfried Echterhoff

Download or read book Crossed Products with Continuous Trace written by Siegfried Echterhoff and published by American Mathematical Soc.. This book was released on 1996 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir presents an extensive study of strongly continuous actions of abelian locally compact groups on [italic capital]C*-algebras with continuous trace. Expositions of the Mackey-Green-Rieffel machine of induced representations and the theory of Morita equivalent [italic capital]C*-dynamical systems are included. There is also an elaboration of the representation theory of crossed products by actions of abelian groups on type I [italic capital]C*-algebras.

Semicrossed Products of Operator Algebras by Semigroups

Author : Kenneth R. Davidson
Publisher : American Mathematical Soc.
ISBN 13 : 147042309X
Total Pages : 97 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Semicrossed Products of Operator Algebras by Semigroups by : Kenneth R. Davidson

Download or read book Semicrossed Products of Operator Algebras by Semigroups written by Kenneth R. Davidson and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors examine the semicrossed products of a semigroup action by -endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.

Geometric and Algebraic Structures in Differential Equations

Author : P.H. Kersten
Publisher : Springer Science & Business Media
ISBN 13 : 9400901798
Total Pages : 346 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Geometric and Algebraic Structures in Differential Equations by : P.H. Kersten

Download or read book Geometric and Algebraic Structures in Differential Equations written by P.H. Kersten and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Bäcklund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.