### The Exponential Rank of Inductive Limit C*-Algebras.

Huaxin Lin, Guihua Gong (1992)

Mathematica Scandinavica

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Huaxin Lin, Guihua Gong (1992)

Mathematica Scandinavica

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Mikael Rordam, Ian F. Putnam (1988)

Mathematica Scandinavica

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Bruce Blackadar, Ola Bratteli (1992)

Mathematische Annalen

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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....

Marius Dadarlat, Terry A. Loring (1994)

Annales de l'institut Fourier

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G. Elliott extended the classification theory of $AF$-algebras to certain real rank zero inductive limits of subhomogeneous ${C}^{*}$-algebras with one dimensional spectrum. We show that this class of ${C}^{*}$-algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the ${K}_{1}$-group. Perturbation and lifting results are provided for certain subhomogeneous ${C}^{*}$-algebras.

Michael Pannenberg (1990)

Mathematica Scandinavica

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Jeremy Lovejoy, Robert Osburn (2010)

Acta Arithmetica

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Marius Dadarlat (1995)

Journal für die reine und angewandte Mathematik

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N. Christopher Phillips (1991)

Mathematica Scandinavica

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Ciatti, Paolo (2000)

Journal of Lie Theory

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Robert J. Archbold, Eberhard Kaniuth (2006)

Studia Mathematica

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Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.

Guihua Gong (1997)

Mathematica Scandinavica

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