The Classification And Structure Of C Algebra Bundles

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The Classification And Structure Of C Algebra Bundles

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Author : Maurice J. Dupré
language : en
Publisher: American Mathematical Soc.
Release Date : 1979

The Classification And Structure Of C Algebra Bundles written by Maurice J. Dupré and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.

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.

An Introduction To C Algebras And The Classification Program

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Author : Karen R. Strung
language : en
Publisher: Springer Nature
Release Date : 2020-12-15

An Introduction To C Algebras And The Classification Program written by Karen R. Strung and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-15 with Mathematics categories.

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.

Operator Algebras And Applications Part 1

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Author : Richard V. Kadison
language : en
Publisher: American Mathematical Soc.
Release Date : 1982

Operator Algebras And Applications Part 1 written by Richard V. Kadison and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.

Characterizations Of C Algebras

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Author : Robert Doran
language : en
Publisher: CRC Press
Release Date : 2018-05-11

Characterizations Of C Algebras written by Robert Doran and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-11 with Mathematics categories.

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.

Representations Of Algebras Locally Compact Groups And Banach Algebraic Bundles

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Author : J. M.G. Fell
language : en
Publisher: Academic Press
Release Date : 1988-04-15

Representations Of Algebras Locally Compact Groups And Banach Algebraic Bundles written by J. M.G. Fell and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-04-15 with Mathematics categories.

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.

Crossed Products Of C Algebras

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Author : Dana P. Williams
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Crossed Products Of C Algebras written by Dana P. Williams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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.

Classification And Structure Theory Of Lie Algebras Of Smooth Sections

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Author : Hasan Gündoğan
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2011

Classification And Structure Theory Of Lie Algebras Of Smooth Sections written by Hasan Gündoğan and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

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.

C Algebras And Elliptic Theory

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Author : Bogdan Bojarski
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-09

C Algebras And Elliptic Theory written by Bogdan Bojarski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-09 with Mathematics categories.

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.

Classification Of Ring And C Ast Algebra Direct Limits Of Finite Dimensional Semisimple Real Algebras

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Author : K. R. Goodearl
language : en
Publisher: American Mathematical Soc.
Release Date : 1987

Classification Of Ring And C Ast Algebra Direct Limits Of Finite Dimensional Semisimple Real Algebras written by K. R. Goodearl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

Motivated by (i) Elliott's classification of direct limits of countable sequences of finite-dimensional semisimple complex algebras and complex AF C*-algebras, (ii) classical results classifying involutions on finite-dimensional semisimple complex algebras, and (iii) the classification by Handelman and Rossmann of automorphisms of period two on the algebras appearing in (i) we study the real algebras described above and completely classify them, up to isomorphism, Morita equivalence, or stable isomorphism. We also show how our classification easily distinguishes various types of algebras within the given classes, and we partially solve the problem of determining exactly which values are attained by the invariants used in classifying these algebras.

C Semigroup Bundles And C Algebras Whose Irreducible Representations Are All Finite Dimensional

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Author : Thomas Karl Müller
language : en
Publisher:
Release Date : 1990

C Semigroup Bundles And C Algebras Whose Irreducible Representations Are All Finite Dimensional written by Thomas Karl Müller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with C*-algebras categories.