The classification of simple separable unital locally ASH algebras

Abstract

Let $A$ be a simple separable unital locally approximately subhomogeneous C*-algebra (locally ASH algebra). It is shown that $A\otimes Q$ can be tracially approximated by unital Elliott-Thomsen algebras with trivial ${\text{K}}_1$-group, where $Q$ is the universal UHF algebra. In particular, it follows that $A$ is classifiable by the Elliott invariant if $A$ is Jiang-Su stable.

40 pages

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