The classification of simple separable unital [formula omitted]-stable locally ASH algebras

Abstract

Let A be a unital simple separable locally approximately subhomogeneous C*-algebra (locally ASH algebra). It is shown that A⊗Q can be tracially approximated by unital Elliott–Thomsen algebras with trivial K1-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.