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 Download
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Author: Cristian Ivanescu
Publisher: Library and Archives Canada = Bibliothèque et Archives Canada
ISBN: 9780612944046
Category :
Languages : en
Pages : 226
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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.
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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.
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.
Author: Liangqing Li
Publisher: American Mathematical Soc.
ISBN: 0821805967
Category : Mathematics
Languages : en
Pages : 138
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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: Luis Santiago Moreno
Publisher:
ISBN: 9780494447666
Category : Mathematics
Languages : en
Pages : 142
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This thesis is a contribution to the classification program for C*-algebras. In a recent paper of Ciuperca and Elliott--that relied on previous work of Thomsen--a classification of all inductive limits of interval algebras was obtained using the Cuntz semigroup as the classification invariant. It is shown in this thesis that the Cuntz semigroup may be used to classify a broader class of C*-algebras: the inductive limits of interval algebras with splitting points at the endpoints. It is shown that any isomorphism between the Cuntz semigroups of two such algebras that preserves a suitable scale may be lifted to an isomorphism between the algebras. The non-Hausdorffness of the spectrum of the splitting interval algebras raises new difficulties that were not present in the interval case. In proving the Isomorphism Theorem just stated, a number of results of interest in their own right are obtained, e.g., a computation is obtained of the Cuntz semigroup of all splitting tree algebras. A homomorphism theorem is also obtained.
Author: Tosio Kato
Publisher: Springer Science & Business Media
ISBN: 3662126788
Category : Mathematics
Languages : en
Pages : 610
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Author: Klaus Thomsen
Publisher:
ISBN:
Category : C*-algebras
Languages : en
Pages : 144
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In this work, it is shown that the Elliott invariant is a complete invariant for the simple unital $C^*$-algebras which can be realized as an inductive limit of a sequence of finite direct sums of algebras of the form $\{f\in C(\mathbb T) \oplus M_n\: f(x_i)\in M_d, i= 1, 2,\dots, N\}$, where $x_1, x_2,\dots, x_N$ is an arbitrary (finite) set on the circle $\mathbb T$ and $d$ is a natural number dividing $n$. The corresponding range of invariants is identified and the classification result is extended to the non-unital case. A series of results about the structure of these $C^*$-algebras and the maps between them are also obtained.
Author: Huaxin Lin
Publisher: American Mathematical Soc.
ISBN: 9780821862889
Category : Mathematics
Languages : en
Pages : 132
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does not need NBB copy
Author: Toan Minh Ho
Publisher:
ISBN: 9780494219171
Category :
Languages : en
Pages : 168
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Book Description
A class of C*-algebras which can be written as inductive limits of homogeneous C*-algebras with diagonal morphisms between their building blocks is studied. A generalization of Urysohn's Lemma is established and used to show such an algebra has the approximately constant eigenvalue map property if, and only if, it is simple. Some applications of this equivalence, namely, every simple algebra in this class has stable rank one and the property SP, are presented. Any simple AH algebra with slow dimension growth also has the property SP. Chapter 4 discusses a form of uniqueness theorem: an inductive limit of homogeneous C*-algebras whose spectra are compact subsets of R is unchanged when we relabel (by means of continuously varying permutations) the eigenvalue patterns of the morphisms between the building blocks. This statement still holds when the spectra of the building blocks are more general compact metric spaces, provided certain conditions hold. A necessary and sufficient condition for a simple algebra in the class under consideration to have real rank zero provided certain conditions hold is also given. (This condition is known in the special case of Goodearl algebras.).
Author: Hongbing Su
Publisher: American Mathematical Soc.
ISBN: 9780821862704
Category : Mathematics
Languages : en
Pages : 100
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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: Adele Zucchi
Publisher:
ISBN: 9780821805954
Category : Functional analysis
Languages : en
Pages : 52
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