One-Parameter Continuous Fields of Kirchberg Algebras
نویسندگان
چکیده
We prove that all unital separable continuous fields of C*-algebras over [0, 1] with fibers isomorphic to the Cuntz algebra On (2 ≤ n ≤ ∞) are trivial. More generally, we show that if A is a separable, unital or stable, continuous field over [0, 1] of Kirchberg C*-algebras satisfying the UCT and having finitely generated K-theory groups, then A is isomorphic to a trivial field if and only if the associated K-theory presheaf is trivial. For fixed d ∈ {0, 1} we also show that, under the additional assumption that the fibers have torsion free Kd -group and trivial Kd+1-group, the Kd -sheaf is a complete invariant for separable stable continuous fields of Kirchberg algebras.
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