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

Author : K. R. Goodearl,David Handelman
Publisher : American Mathematical Soc.
Page : 147 pages
File Size : 45,5 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821824351

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Classification of Ring and $C^\ast $-Algebra Direct Limits of Finite-Dimensional Semisimple Real Algebras by K. R. Goodearl,David Handelman Pdf

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.

Author : Edward G. Effros
Publisher : American Mathematical Soc.
Page : 74 pages
File Size : 49,6 Mb
Release : 1981
Category : Mathematics
ISBN : 9780821816974

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Dimensions and C*-algebras by Edward G. Effros Pdf

This book is largely devoted to the most elementary algebras and $C^*$-algebras, namely those which are direct limits of complex semisimple algebras.

Author : Ambar N. Sengupta
Publisher : Springer Science & Business Media
Page : 383 pages
File Size : 48,5 Mb
Release : 2011-12-08
Category : Mathematics
ISBN : 9781461412304

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Representing Finite Groups by Ambar N. Sengupta Pdf

This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviting. Central concepts are revisited and explored from multiple viewpoints. Exercises at the end of the chapter help reinforce the material. Representing Finite Groups: A Semisimple Introduction would serve as a textbook for graduate and some advanced undergraduate courses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A final chapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematics and mathematical physics will also find this book useful. A separate solutions manual is available for instructors.

Author : Hongbing Su
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 50,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821826072

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On the Classification of $C^*$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs by Hongbing Su Pdf

This work shows that $K$-theoretic data is a complete invariant for certain inductive limit $C^*$-algebras. $C^*$-algebras of this kind are useful in studying group actions. Su gives a $K$-theoretic classification of the real rank zero $C^*$-algebras that can be expressed as inductive limits of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs or Hausdorff one-dimensional spaces defined as inverse limits of finite graphs. In addition, Su establishes a characterization for an inductive limit of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs to be real rank zero.

Author : Liangqing Li
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 40,6 Mb
Release : 1997
Category : C*-algebras
ISBN : 9780821805961

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Classification of Simple $C$*-algebras: Inductive Limits of Matrix Algebras over Trees by Liangqing Li Pdf

In this paper, it is shown that the simple unital C*-algebras arising as inductive limits of sequences of finite direct sums of matrix algebras over [italic capital]C([italic capital]X[subscript italic]i), where [italic capital]X[subscript italic]i are arbitrary variable trees, are classified by K-theoretical and tracial data. This result generalizes the result of George Elliott of the case of [italic capital]X[subscript italic]i = [0, 1]. The added generality is useful in the classification of more general inductive limit C*-algebras.

Author : Anonim
Publisher : Unknown
Page : 1160 pages
File Size : 54,8 Mb
Release : 2009
Category : Editions
ISBN : STANFORD:36105129044140

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Guide to Reprints by Anonim Pdf

Author : Lance W. Small
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 50,5 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821815250

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Noetherian Rings and Their Applications by Lance W. Small Pdf

Researchers in ring theory or allied topics, such as the representation theory of finite dimensional Lie algebras, will appreciate this collection of expository lectures on advances in ring theory and their applications to other areas. Five of the lectures were delivered at a conference on Noetherian rings at the Mathematisches Forschungsinstitut, Oberwolfach, in January 1983, and the sixth was delivered at a London Mathematical Society Durham conference in July 1983. The study of the prime and primitive ideal spectra of various classes of rings forms a common theme in the lectures, and they touch on such topics as the structure of group rings of polycyclic-by-finite groups, localization in non commutative rings, and rings of differential operators. The lectures require the background of an advanced graduate student in ring theory and may be used in seminars in ring theory at this level.

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 41,8 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698

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An Introduction to Lie Groups and Lie Algebras by Alexander A. Kirillov Pdf

Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Author : Huaxin Lin,Norman Christopher Phillips
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 46,9 Mb
Release : 1995
Category : Mathematics
ISBN : 082186288X

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Classification of Direct Limits of Even Cuntz-circle Algebras by Huaxin Lin,Norman Christopher Phillips Pdf

does not need NBB copy

Author : Anonim
Publisher : Unknown
Page : 1208 pages
File Size : 41,7 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015078588608

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Mathematical Reviews by Anonim Pdf

Author : Yurj A. Drozd,Vladimir V. Kirichenko
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642762444

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Finite Dimensional Algebras by Yurj A. Drozd,Vladimir V. Kirichenko Pdf

This English edition has an additional chapter "Elements of Homological Al gebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only metic ulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface The theory of finite dimensional algebras is one of the oldest branches of modern algebra. Its origin is linked to the work of Hamilton who discovered the famous algebra of quaternions, and Cayley who developed matrix theory. Later finite dimensional algebras were studied by a large number of mathematicians including B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. At the end of the last century T. Molien and E. Cartan described the semisimple algebras over the complex and real fields and paved the first steps towards the study of non-semi simple algebras.

Author : Sonia Natale
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 45,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821839485

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Semisolvability of Semisimple Hopf Algebras of Low Dimension by Sonia Natale Pdf

The author proves that every semisimple Hopf algebra of dimension less than $60$ over an algebraically closed field $k$ of characteristic zero is either upper or lower semisolvable up to a cocycle twist.

Author : Peter Webb
Publisher : Cambridge University Press
Page : 339 pages
File Size : 54,5 Mb
Release : 2016-08-19
Category : Mathematics
ISBN : 9781107162396

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A Course in Finite Group Representation Theory by Peter Webb Pdf

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.

Author : Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 42,9 Mb
Release : 2016-08-05
Category : Algebraic topology
ISBN : 9781470434410

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Tensor Categories by Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik Pdf

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Author : American Mathematical Society
Publisher : Unknown
Page : 402 pages
File Size : 43,7 Mb
Release : 1981
Category : Electronic journals
ISBN : UCAL:B3647858

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Notices of the American Mathematical Society by American Mathematical Society Pdf