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The Classification And Structure Of C Algebra Bundles
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Book Synopsis The Classification and Structure of C^*-Algebra Bundles by : Maurice J. Dupré
Download or read book The Classification and Structure of C^*-Algebra Bundles written by Maurice J. Dupré and published by American Mathematical Soc.. This book was released on 1979 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objects of study in this paper are certain fibre spaces which arise naturally in the representation theory of C*-algebras and locally compact groups. These are a type of Banach bundle, all of whose fibres are C*-algebras. The main aim of this paper is to give a pasting homotopy type classification theory for certain classes of C*-bundles having primarily finite-dimensional fibres and thus classifying the resulting second-order bundles.
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.
Book Synopsis Operator Algebras and Applications, Part 1 by : Richard V. Kadison
Download or read book Operator Algebras and Applications, Part 1 written by Richard V. Kadison and published by American Mathematical Soc.. This book was released on 1982 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Characterizations of C* Algebras by : Robert Doran
Download or read book Characterizations of C* Algebras written by Robert Doran and published by CRC Press. This book was released on 2018-05-11 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified, in-depth discussion of the now classical Gelfand-Naimark theorems, thiscomprehensive text assesses the current status of modern analysis regarding both Banachand C*-algebras.Characterizations of C*-Algebras: The Gelfand-Naimark Theorems focuses on general theoryand basic properties in accordance with readers' needs ... provides complete proofs of theGelfand-Naimark theorems as well as refinements and extensions of the original axioms. . . gives applications of the theorems to topology, harmonic analysis. operator theory.group representations, and other topics ... treats Hermitian and symmetric *-algebras.algebras with and without identity, and algebras with arbitrary (possibly discontinuous)involutions . . . includes some 300 end-of-chapter exercises . . . offers appendices on functionalanalysis and Banach algebras ... and contains numerous examples and over 400 referencesthat illustrate important concepts and encourage further research.Characterizations of C*-Algebras: The Gelfand-Naimark Theorems is an ideal text for graduatestudents taking such courses as The Theory of Banach Algebras and C*-Algebras: inaddition , it makes an outstanding reference for physicists, research mathematicians in analysis,and applied scientists using C*-algebras in such areas as statistical mechanics, quantumtheory. and physical chemistry.
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.
Book Synopsis Classification and Structure Theory of Lie Algebras of Smooth Sections by : Hasan Gündoğan
Download or read book Classification and Structure Theory of Lie Algebras of Smooth Sections written by Hasan Gündoğan and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups and their "derived objects", Lie algebras, appear in various fields of mathematics and physics. At least since the beginning of the 20th century, and after the famous works of Wilhelm Killing, Elie Cartan, Eugenio Elia Levi, Anatoly Malcev and Igor Ado on the structure of finite-dimensional Lie algebras, the classification and structure theory of infinite-dimensional Lie algebras has become an interesting and fairly vast field of interest. This dissertation focusses on the structure of Lie algebras of smooth and k-times differentiable sections of finite-dimensional Lie algebra bundles, which are generalizations of the famous and well-understood affine Kac-Moody algebras. Besides answering the immediate structural questions (center, commutator algebra, derivations, centroid, automorphism group), this work approaches a classification of section algebras by homotopy theory. Furthermore, we determine a universal invariant symmetric bilinear form on Lie algebras of smooth sections and use this form to define a natural central extension which is universal, at least in the case of Lie algebra bundles with compact base manifold.
Book Synopsis C*-algebras and Elliptic Theory by : Bogdan Bojarski
Download or read book C*-algebras and Elliptic Theory written by Bogdan Bojarski and published by Springer Science & Business Media. This book was released on 2006-11-09 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.
Book Synopsis C*-semigroup Bundles and C*-algebras Whose Irreducible Representations are All Finite Dimensional by : Thomas Karl Müller
Download or read book C*-semigroup Bundles and C*-algebras Whose Irreducible Representations are All Finite Dimensional written by Thomas Karl Müller and published by . This book was released on 1990 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles by : J. M.G. Fell
Download or read book Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles written by J. M.G. Fell and published by Academic Press. This book was released on 1988-05-01 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.
Book Synopsis Banach Bundles, Banach Modules, and Automorphisms of C*-algebras by : Maurice J. Dupré
Download or read book Banach Bundles, Banach Modules, and Automorphisms of C*-algebras written by Maurice J. Dupré and published by Pitman Advanced Publishing Program. This book was released on 1983 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Recent Advances in Operator Theory, Operator Algebras, and their Applications by : Dumitru Gaspar
Download or read book Recent Advances in Operator Theory, Operator Algebras, and their Applications written by Dumitru Gaspar and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.
Book Synopsis Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory by : Robert S. Doran
Download or read book Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 1991 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented at the NSF/CBMS Regional Conference on Coordinates in Operator Algebras, held at Texas Christian University in Fort Worth in May 1990. During the conference, in addition to a series of ten lectures by Paul S Muhly (which will be published in a CBMS Regional Conference Series volume), there were twenty-eight lectures delivered by conference participants on a broad range of topics of current interest in operator algebras and operator theory. This volume contains slightly expanded versions of most of those lectures. Participants were encouraged to bring open problems to the conference, and, as a result, there are over one hundred problems and questions scattered throughout this volume. Readers will appreciate this book for the overview it provides of current topics and methods of operator algebras and operator theory.
Book Synopsis Basic Bundle Theory and K-Cohomology Invariants by : Dale Husemöller
Download or read book Basic Bundle Theory and K-Cohomology Invariants written by Dale Husemöller and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory. It aims to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, comes from quantum field theory, where topological invariants play an important role.
Download or read book Dissertationes Mathematicae written by and published by . This book was released on 1966 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rozprawy Matematyczne written by and published by . This book was released on 1989 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Associative and Non-Commutative Algebra and Operator Theory by : Cheikh Thiécoumbe Gueye
Download or read book Non-Associative and Non-Commutative Algebra and Operator Theory written by Cheikh Thiécoumbe Gueye and published by Springer. This book was released on 2016-11-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he has served as a mentor to a generation of mathematicians in Senegal and around the world.
Book Synopsis Geometry of Differential Forms by : Shigeyuki Morita
Download or read book Geometry of Differential Forms written by Shigeyuki Morita and published by American Mathematical Soc.. This book was released on 2001 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated is a detailed description of the Chern-Weil theory. The book can serve as a textbook for undergraduate students and for graduate students in geometry.
