Inductive limits of semiprojective C*algebras
Abstract
We prove closure properties for the class of C*algebras that are inductive limits of semiprojective C*algebras. Most importantly, we show that this class is closed under shape domination, and so in particular under shape and homotopy equivalence. It follows that the considered class is quite large. It contains for instance the stable suspension of any nuclear C*algebra satisfying the UCT and with torsionfree $K_0$group. In particular, the stabilized C*algebra of continuous functions on the pointed sphere is isomorphic to an inductive limit of semiprojectives.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.04908
 Bibcode:
 2018arXiv180404908T
 Keywords:

 Mathematics  Operator Algebras;
 Primary 46L05;
 46M10;
 Secondary 46L85;
 46M20;
 54C55;
 54C56;
 55M15;
 55P55
 EPrint:
 17 pages