Dimensions And C Ast Algebras

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Dimensions And C Ast Algebras

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Author : Edward G. Effros
language : en
Publisher: American Mathematical Soc.
Release Date : 1981

Dimensions And C Ast Algebras written by Edward G. Effros 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 1981 with Mathematics categories.

Discusses elementary algebras and $C DEGREES*$-algebras, namely those which are direct limits of complex semi simple al

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.

Covering Dimension Of C Algebras And 2 Coloured Classification

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Author : Joan Bosa
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-02-21

Covering Dimension Of C Algebras And 2 Coloured Classification written by Joan Bosa 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 2019-02-21 with Mathematics categories.

The authors introduce the concept of finitely coloured equivalence for unital -homomorphisms between -algebras, for which unitary equivalence is the -coloured case. They use this notion to classify -homomorphisms from separable, unital, nuclear -algebras into ultrapowers of simple, unital, nuclear, -stable -algebras with compact extremal trace space up to -coloured equivalence by their behaviour on traces; this is based on a -coloured classification theorem for certain order zero maps, also in terms of tracial data. As an application the authors calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, -stable -algebras with compact extremal trace space: it is 1. In the case that the extremal trace space also has finite topological covering dimension, this confirms the remaining open implication of the Toms-Winter conjecture. Inspired by homotopy-rigidity theorems in geometry and topology, the authors derive a “homotopy equivalence implies isomorphism” result for large classes of -algebras with finite nuclear dimension.

An Introduction To K Theory For C Algebras

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Author : M. Rørdam
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-20

An Introduction To K Theory For C Algebras written by M. Rørdam and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-20 with Mathematics categories.

This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.

Recent Advances In The Representation Theory Of Rings And C Ast Algebras By Continuous Sections

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Author : John R. Liukkonen
language : en
Publisher: American Mathematical Soc.
Release Date : 1974

Recent Advances In The Representation Theory Of Rings And C Ast Algebras By Continuous Sections written by John R. Liukkonen 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 1974 with Mathematics categories.

From March 20 through April 5, 1973, the Mathematics Department of Tulane University organized a seminar on recent progress made in the general theory of the representation of rings and topological algebras by continuous sections in sheaves and bundles. The seminar was divided into two main sections: one concerned with sheaf representation, the other with bundle representation. The first was concerned with ringed spaces, applications to logic, universal algebra and lattice theory. The second was almost exclusively devoted to C*-algebra and Hilbert space bundles or closely related material. This collection represents the majority of the papers presented by seminar participants, with the addition of three papers which were presented by title.

Operator Algebras

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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-19

Operator Algebras written by Ola Bratteli 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 2007-01-19 with Mathematics categories.

The theme of the first Abel Symposium was operator algebras in a wide sense. In the last 40 years operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as "non-commutative geometry". It has branched out in several sub-disciplines and made contact with other subjects. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics reflect to some extent how the subject has developed. This is the first volume in a prestigious new book series linked to the Abel prize.

Matrix Algebra

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Author : James E. Gentle
language : en
Publisher: Springer Nature
Release Date : 2024-03-07

Matrix Algebra written by James E. Gentle and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-07 with Mathematics categories.

This book presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra. Matrix algebra is one of the most important areas of mathematics in data science and in statistical theory, and previous editions had essential updates and comprehensive coverage on critical topics in mathematics. This 3rd edition offers a self-contained description of relevant aspects of matrix algebra for applications in statistics. It begins with fundamental concepts of vectors and vector spaces; covers basic algebraic properties of matrices and analytic properties of vectors and matrices in multivariate calculus; and concludes with a discussion on operations on matrices, in solutions of linear systems and in eigenanalysis. It also includes discussions of the R software package, with numerous examples and exercises. Matrix Algebra considers various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes special properties of those matrices; as well as describing various applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. It begins with a discussion of the basics of numerical computations and goes on to describe accurate and efficient algorithms for factoring matrices, how to solve linear systems of equations, and the extraction of eigenvalues and eigenvectors. It covers numerical linear algebra—one of the most important subjects in the field of statistical computing. The content includes greater emphases on R, and extensive coverage of statistical linear models. Matrix Algebra is ideal for graduate and advanced undergraduate students, or as a supplementary text for courses in linear models or multivariate statistics. It’s also ideal for use in a course in statistical computing, or as a supplementary text forvarious courses that emphasize computations.

Lie Algebras Part 2

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Author : E.A. de Kerf
language : en
Publisher: Elsevier
Release Date : 1997-10-30

Lie Algebras Part 2 written by E.A. de Kerf and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-30 with Science categories.

This is the long awaited follow-up to Lie Algebras, Part I which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part II deals mainly with the representations and applications of Lie Algebras and contains many cross references to Part I.The theoretical part largely deals with the representation theory of Lie algebras with a triangular decomposition, of which Kac-Moody algebras and the Virasoro algebra are prime examples. After setting up the general framework of highest weight representations, the book continues to treat topics as the Casimir operator and the Weyl-Kac character formula, which are specific for Kac-Moody algebras.The applications have a wide range. First, the book contains an exposition on the role of finite-dimensional semisimple Lie algebras and their representations in the standard and grand unified models of elementary particle physics. A second application is in the realm of soliton equations and their infinite-dimensional symmetry groups and algebras. The book concludes with a chapter on conformal field theory and the importance of the Virasoro and Kac-Moody algebras therein.

Mass Dimension One Fermions

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Author : Dharam Ahluwalia
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-04

Mass Dimension One Fermions written by Dharam Ahluwalia and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-04 with Science categories.

Provides an overview of the eigenspinors of the charge conjugation operator and mass one dimension fermions.

Introduction To Operator Algebras

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Author : Bing-Ren Li
language : en
Publisher: World Scientific
Release Date : 1992

Introduction To Operator Algebras written by Bing-Ren Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students.