The Exponential Rank of Inductive Limit C*-Algebras.

Huaxin Lin; Guihua Gong

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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....

Extensions of certain real rank zero $C^{*}$ -algebras

Marius Dadarlat, Terry A. Loring (1994)

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G. Elliott extended the classification theory of $A F$ -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.