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On The Classification Of C Algebras Of Real Rank Zero Microform Inductive Limits Of Matrix Algebras Over Non Hausdorff Graphs Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of On The Classification Of C Algebras Of Real Rank Zero Microform Inductive Limits Of Matrix Algebras Over Non Hausdorff Graphs book. This book definitely worth reading, it is an incredibly well-written.
Author : Hongbing Su
Publisher : National Library of Canada = Bibliothèque nationale du Canada
Page : 128 pages
File Size : 52,7 Mb
Release : 1992
Category : Electronic
ISBN : 0315787503
Author : Hongbing Su
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 54,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821826072
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 : 50,9 Mb
Release : 1997
Category : C*-algebras
ISBN : 9780821805961
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 : Cristian Ivanescu
Publisher : Library and Archives Canada = Bibliothèque et Archives Canada
Page : 226 pages
File Size : 44,9 Mb
Release : 2004
Category : Electronic
ISBN : 0612944042
A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have spectrum homeomorphic to the closed interval [0, 1] or to a finite disjoint union of closed intervals. In particular, a classification of those stably AI algebras which are inductive limits of hereditary sub-C*-algebras of interval algebras is obtained. Also, the range of the invariant is calculated.
Author : Anonim
Publisher : Unknown
Page : 738 pages
File Size : 44,5 Mb
Release : 1993
Category : Dissertations, Academic
ISBN : STANFORD:36105020027400
Author : Joan Bosa,Nathanial P. Brown,Yasuhiko Sato,Aaron Tikuisis,Stuart White,Wilhelm Winter
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 42,7 Mb
Release : 2019-02-21
Category : C*-algebras
ISBN : 9781470434700
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.
Author : Huaxin Lin,Norman Christopher Phillips
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 46,5 Mb
Release : 1995
Category : Mathematics
ISBN : 082186288X
does not need NBB copy
Author : K. R. Goodearl,David Handelman
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 55,6 Mb
Release : 1987-06-30
Category : Mathematics
ISBN : 0821861034
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 : Maurice J. Dupré
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 49,6 Mb
Release : 1979
Category : Mathematics
ISBN : 9780821822227
Author : Huaxin Lin
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 48,7 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821862731
This work shows that the Weyl-von Neumann theorem for unitaries holds for *s-unital AF-algebras and their multiplier algebras. Lin studies E(X,A) , the quotient of Ext[s]eu(C(X),A) by a special class of trivial extension, dubbed totally trivial extensions. This leads to a BDF-type classification for extensions of C(X) by a *s-unital purely infinite simple C] *-algebra with trivial K[1-group. Lin also shows that, when X is a compact subset of the plane, every extension of C(X) by a finite matroid C]*-algebra is totally trivial. Classification of these extensions for nice spaces is given, as are some other versions of the Weyl-von Neumann-Berg theorem.
Author : Boris Khesin,Robert Wendt
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 43,5 Mb
Release : 2008-09-28
Category : Mathematics
ISBN : 9783540772637
This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.
Author : Arkadij L. Onishchik,Ernest B. Vinberg
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642743344
This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.
Author : Siegfried Bosch
Publisher : Springer
Page : 254 pages
File Size : 52,5 Mb
Release : 2014-08-22
Category : Mathematics
ISBN : 9783319044170
The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 646 pages
File Size : 53,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9780387217529
Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
Author : Dimitry Kozlov
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 46,7 Mb
Release : 2008-01-08
Category : Mathematics
ISBN : 3540730516
This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.
