On the classification of simple inductive limit -algebras. I: The reduction theorem

  • Guihua Gong

    Department of Mathematics University of Puerto Rico, Rio Piedras San Juan, PR 00931-3355, USA
On the classification of simple inductive limit $C^*$-algebras. I: The reduction theorem cover
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Abstract

Suppose that is a simple -algebra, where are compact metrizable spaces of uniformly bounded dimensions (this restriction can be relaxed to a condition of very slow dimension growth). It is proved in this article that can be written as an inductive limit of direct sums of matrix algebras over certain special 3-dimensional spaces. As a consequence it is shown that this class of inductive limit -algebras is classified by the Elliott invariant --- consisting of the ordered K-group and the tracial state space --- in a subsequent paper joint with G. Elliott and L. Li (Part II of this series). (Note that the -algebras in this class do not enjoy the real rank zero property.)

Cite this article

Guihua Gong, On the classification of simple inductive limit -algebras. I: The reduction theorem. Doc. Math. 7 (2002), pp. 255–461

DOI 10.4171/DM/127