Borel complexity and automorphisms of C*-algebras

摘要

We show that if A is Z, O-2, O-infinity, a UHF algebra of infinite type, or the tensor product of a UHF algebra of infinite type and O-infinity, then the conjugation action Aut(A) curved right arrow Aut(A) is generically turbulent for the point-norm topology. We moreover prove that if A is either (i) a separable C*-algebra which is stable under tensoring with Z or K, or (ii) a separable Hi factor which is McDuff or a free product of II1 factors, then the automorphisms of A are not classifiable up to conjugacy by countable structures. (C) 2015 Elsevier Inc. All rights reserved.