Classification Of Ring And C Ast Algebra Direct Limits Of Finite Dimensional Semisimple Real Algebras
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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.
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
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Author : K.R. Goodearl
language : en
Publisher:
Release Date : 1987
Classification Of Ring And C written by K.R. Goodearl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Guide To Reprints
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Author :
language : en
Publisher:
Release Date : 2009
Guide To Reprints written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Editions categories.
Algebras And Representation Theory
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Author : Karin Erdmann
language : en
Publisher: Springer
Release Date : 2018-09-07
Algebras And Representation Theory written by Karin Erdmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-07 with Mathematics categories.
This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.
Forthcoming Books
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Author : Rose Arny
language : en
Publisher:
Release Date : 1988-07
Forthcoming Books written by Rose Arny and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-07 with American literature categories.
Advanced Algebra
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Author : Anthony W. Knapp
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-11
Advanced Algebra written by Anthony W. Knapp 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 2007-10-11 with Mathematics categories.
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.
C Algebras By Example
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Author : Kenneth R. Davidson
language : en
Publisher: American Mathematical Society, Fields Institute
Release Date : 2023-10-04
C Algebras By Example written by Kenneth R. Davidson and has been published by American Mathematical Society, Fields Institute this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-04 with Mathematics categories.
The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of $K$-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty years has been based on a careful study of these special classes. While there are many books on C*-algebras and operator algebras available, this is the first one to attempt to explain the real examples that researchers use to test their hypotheses. Topics include AF algebras, Bunce–Deddens and Cuntz algebras, the Toeplitz algebra, irrational rotation algebras, group C*-algebras, discrete crossed products, abelian C*-algebras (spectral theory and approximate unitary equivalence) and extensions. It also introduces many modern concepts and results in the subject such as real rank zero algebras, topological stable rank, quasidiagonality, and various new constructions. These notes were compiled during the author's participation in the special year on C*-algebras at The Fields Institute for Research in Mathematical Sciences during the 1994–1995 academic year. The field of C*-algebras touches upon many other areas of mathematics such as group representations, dynamical systems, physics, $K$-theory, and topology. The variety of examples offered in this text expose the student to many of these connections. Graduate students with a solid course in functional analysis should be able to read this book. This should prepare them to read much of the current literature. This book is reasonably self-contained, and the author has provided results from other areas when necessary.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2007
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
A Course In Finite Group Representation Theory
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Author : Peter Webb
language : en
Publisher: Cambridge University Press
Release Date : 2016-08-19
A Course In Finite Group Representation Theory written by Peter Webb 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 2016-08-19 with Mathematics categories.
This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.