On the classification of C*-algebras of real rank zero.
George A. Elliott (1993)
Journal für die reine und angewandte Mathematik
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George A. Elliott (1993)
Journal für die reine und angewandte Mathematik
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Klaus Thomsen (1988)
Journal für die reine und angewandte Mathematik
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Bruce Blackadar, Ola Bratteli (1992)
Mathematische Annalen
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Mikael Rordam (1993)
Journal für die reine und angewandte Mathematik
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Marius Dadarlat, Terry A. Loring (1994)
Annales de l'institut Fourier
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G. Elliott extended the classification theory of -algebras to certain real rank zero inductive limits of subhomogeneous -algebras with one dimensional spectrum. We show that this class of -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the -group. Perturbation and lifting results are provided for certain subhomogeneous -algebras.
B. Blackadar, M. Dadarlat, M. Rordam (1991)
Mathematica Scandinavica
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Ian F. Putnam (1990)
Journal für die reine und angewandte Mathematik
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Kenneth R. Goodearl (1992)
Publicacions Matemàtiques
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A construction method is presented for a class of simple C*-algebras whose basic properties -including their real ranks- can be computed relatively easily, using linear algebra. A numerival invariant attached to the construction determines wether a given algebra has real rank 0 or 1. Moreover, these algebras all have stable rank 1, and each nonzero hereditary sub-C*-algebra contains a nonzero projection, yet there are examples in which the linear span of the projections is not dense....
Andrzej Skowronski, Josef Waschbüsch (1983)
Journal für die reine und angewandte Mathematik
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T. Giordano (1988)
Journal für die reine und angewandte Mathematik
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Marius Dadarlat, Terry A. Loring (1996)
Mathematische Annalen
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P. W. Ng (2009)
Studia Mathematica
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Let 𝓐 be a unital separable simple nuclear C*-algebra such that ℳ (𝓐 ⊗ 𝓚) has real rank zero. Suppose that ℂ is a separable simple liftable and purely large unital C*-subalgebra of ℳ (𝓐 ⊗ 𝓚)/ (𝓐 ⊗ 𝓚). Then the relative double commutant of ℂ in ℳ (𝓐 ⊗ 𝓚)/(𝓐 ⊗ 𝓚) is equal to ℂ.
Eberhard Kirchberg (1994)
Journal für die reine und angewandte Mathematik
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