A CLASSIFICATION OF NON-SIMPLE C*-ALGEBRAS OF TRACIAL RANK ONE:   INDUCTIVE LIMITS OF FINITE DIRECT SUMS OF SIMPLE TAI C*-ALGEBRAS

Jiang Chunlan<sup>*</sup>

doi:10.1142/S1793525311000593

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A CLASSIFICATION OF NON-SIMPLE C-ALGEBRAS OF TRACIAL RANK ONE: INDUCTIVE LIMITS OF FINITE DIRECT SUMS OF SIMPLE TAI C-ALGEBRAS

作者：Jiang Chunlan^*

来源：Journal of Topology and Analysis, 2011, 3(3): 385-404.

DOI：10.1142/S1793525311000593

摘要

In this paper, we will classify the class of C*-algebras which are inductive limits of finite direct sums of unital simple separable nuclear C*-algebras with tracial rank no more than one (or equivalently TAI algebras) with torsion K(1)-group which satisfy the UCT. The invariant consists of ordered total K-theory and the tracial state spaces of cutdown algebras (with certain compatibility conditions).