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On the Classification of C*-algebras of Real Rank Zero [microform] : Inductive Limits of Matrix Algebras Over Non-Hausdorff Graphs

On the Classification of C*-algebras of Real Rank Zero [microform] : Inductive Limits of Matrix Algebras Over Non-Hausdorff Graphs PDF Author: Hongbing Su
Publisher: National Library of Canada = Bibliothèque nationale du Canada
ISBN: 9780315787506
Category :
Languages : en
Pages :

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On the Classification of C*-algebras of Real Rank Zero [microform] : Inductive Limits of Matrix Algebras Over Non-Hausdorff Graphs

On the Classification of C*-algebras of Real Rank Zero [microform] : Inductive Limits of Matrix Algebras Over Non-Hausdorff Graphs PDF Author: Hongbing Su
Publisher: National Library of Canada = Bibliothèque nationale du Canada
ISBN: 9780315787506
Category :
Languages : en
Pages :

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

On the Classification of $C^*$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs PDF Author: Hongbing Su
Publisher: American Mathematical Soc.
ISBN: 0821826077
Category : Mathematics
Languages : en
Pages : 98

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Book Description
In this paper a [italic capital]K-theoretic classification is given of the real rank zero [italic capital]C*-algebras that can be expressed as inductive limits of sequences of finite direct sums of matrix algebras over finite connected graphs (possibly with multiple vertices). The special case that the graphs are circles is due to Elliott.

On the Classicifcation on C*-algebras of Real Rank Zero

On the Classicifcation on C*-algebras of Real Rank Zero PDF Author: Hongbing Su
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Classification of Simple $C$*-algebras: Inductive Limits of Matrix Algebras over Trees

Classification of Simple $C$*-algebras: Inductive Limits of Matrix Algebras over Trees PDF Author: Liangqing Li
Publisher: American Mathematical Soc.
ISBN: 0821805967
Category : Mathematics
Languages : en
Pages : 138

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Book Description
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.

An Introduction to the Classification of Amenable C*-algebras

An Introduction to the Classification of Amenable C*-algebras PDF Author: Huaxin Lin
Publisher: World Scientific
ISBN: 9789812799883
Category : Mathematics
Languages : en
Pages : 336

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Book Description
The theory and applications of C Oeu -algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C Oeu -algebras is also regarded as non-commutative topology. About a decade ago, George A. Elliott initiated the program of classification of C Oeu -algebras (up to isomorphism) by their K -theoretical data. It started with the classification of AT -algebras with real rank zero. Since then great efforts have been made to classify amenable C Oeu -algebras, a class of C Oeu -algebras that arises most naturally. For example, a large class of simple amenable C Oeu -algebras is discovered to be classifiable. The application of these results to dynamical systems has been established. This book introduces the recent development of the theory of the classification of amenable C Oeu -algebras OCo the first such attempt. The first three chapters present the basics of the theory of C Oeu -algebras which are particularly important to the theory of the classification of amenable C Oeu -algebras. Chapter 4 otters the classification of the so-called AT -algebras of real rank zero. The first four chapters are self-contained, and can serve as a text for a graduate course on C Oeu -algebras. The last two chapters contain more advanced material. In particular, they deal with the classification theorem for simple AH -algebras with real rank zero, the work of Elliott and Gong. The book contains many new proofs and some original results related to the classification of amenable C Oeu -algebras. Besides being as an introduction to the theory of the classification of amenable C Oeu -algebras, it is a comprehensive reference for those more familiar with the subject. Sample Chapter(s). Chapter 1.1: Banach algebras (260 KB). Chapter 1.2: C*-algebras (210 KB). Chapter 1.3: Commutative C*-algebras (212 KB). Chapter 1.4: Positive cones (207 KB). Chapter 1.5: Approximate identities, hereditary C*-subalgebras and quotients (230 KB). Chapter 1.6: Positive linear functionals and a Gelfand-Naimark theorem (235 KB). Chapter 1.7: Von Neumann algebras (234 KB). Chapter 1.8: Enveloping von Neumann algebras and the spectral theorem (217 KB). Chapter 1.9: Examples of C*-algebras (270 KB). Chapter 1.10: Inductive limits of C*-algebras (252 KB). Chapter 1.11: Exercises (220 KB). Chapter 1.12: Addenda (168 KB). Contents: The Basics of C Oeu -Algebras; Amenable C Oeu -Algebras and K -Theory; AF- Algebras and Ranks of C Oeu -Algebras; Classification of Simple AT -Algebras; C Oeu -Algebra Extensions; Classification of Simple Amenable C Oeu -Algebras. Readership: Researchers and graduate students in operator algebras."

On the Classification of

On the Classification of PDF Author: Hongbing Su
Publisher:
ISBN:
Category :
Languages : en
Pages : 83

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On the Classification of Simple C*-algebras which are Inductive Limits of Continuous-trace C*-algebras Whose Spectrum is the Closed Interval [0,1] [microform]

On the Classification of Simple C*-algebras which are Inductive Limits of Continuous-trace C*-algebras Whose Spectrum is the Closed Interval [0,1] [microform] PDF Author: Cristian Ivanescu
Publisher: Library and Archives Canada = Bibliothèque et Archives Canada
ISBN: 9780612944046
Category :
Languages : en
Pages : 226

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Book Description
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.

Classification of Nuclear C*-Algebras. Entropy in Operator Algebras

Classification of Nuclear C*-Algebras. Entropy in Operator Algebras PDF Author: M. Rordam
Publisher: Springer Science & Business Media
ISBN: 3662048256
Category : Mathematics
Languages : en
Pages : 206

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to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. Afactor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.

Classification of Inductive Limits of Continuous Trace C*-Algebras

Classification of Inductive Limits of Continuous Trace C*-Algebras PDF Author: Cristian Ivanescu
Publisher: LAP Lambert Academic Publishing
ISBN: 9783838303253
Category : C*-algebras
Languages : en
Pages : 88

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Book Description
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]. In particular, a classification of simple stably AI algebras is obtained. Also, the range of the invariant is calculated. We start by approximating the building blocks appearing in a given inductive limit decomposition by certain special building blocks. The special building blocks are continuous trace C*-algebras with finite dimensional irreducible representations and such that the dimension of the representations, as a function on the interval, is a finite (lower semicontinuous) step function. It is then proved that these C*-algebras have finite presentations and stable relations. The advantage of having inductive limits of special subhomogeneous algebras is that we can prove the existence of certain gaps for the induced maps between the affine function spaces. These gaps are necessary to prove the Existence Theorem. Also the Uniqueness theorem is proved for these special building blocks.

Classification of Ring and $C^\ast $-Algebra Direct Limits of Finite-Dimensional Semisimple Real Algebras

Classification of Ring and $C^\ast $-Algebra Direct Limits of Finite-Dimensional Semisimple Real Algebras PDF Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 082182435X
Category : Mathematics
Languages : en
Pages : 161

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Book Description
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.