One-parameter continuous fields of Kirchberg algebras (Q2472481)

A Kirchberg algebra is a separable nuclear purely infinite simple \(C^*\)-algebra. The authors show that a separable, unital or stable, continuous field over \([0,1]\) of Kirchberg algebras satisfying the UCT and having finitely generated \(K\)-theory groups is isomorphic to a trivial field iff the associated \(K\)-theory presheaf is trivial. It is also shown that the \(K_d\)-sheaf, \(d\in\mathbb Z/2\mathbb Z\), is a complete invariant for separable stable continuous fields of Kirchberg algebras if the \(K_d\)-groups of the fibers are torsion free and the \(K_{d+1}\)-groups are trivial. As a corollary, it is shown that unital separable continuous fields of \(C^*\)-algebras over \([0,1]\) with fibers isomorphic to the Cuntz algebra \(\mathcal O_n\) (\(2\leq n\leq\infty\)) are trivial.