In this article we survey some of the recent goings-on in the classification programme of C-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott conjecture does not hold at its boldest. We review the construction of this object both by means of positive elements and via its recent interpretation using counta...

Let A be a simple separable unital 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.

http://dx.doi.org/10.1016/j.pocean.2016.01.004 0079-6611/ 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +1 707 781 2555 x304. E-mail addresses: [email protected] (R.E. Fontana), melliott@pointblue. org (M.L. Elliott), [email protected] (J.L. Largier), [email protected] (J. Jahncke). Rachel E. Fontana , Meredith L. Elliott b,⇑, John L. Largier , Jaime Jahncke b