Analysis seminar

Martino Lupini, York University

“The complexity of the relation of unitary equivalence for automorphisms of separable unital C*-algebras”

A classical result of Glimm from 1961 asserts that the irreducible
representations of a given separable C*-algebra A are classifiable by real
numbers up to unitary equivalence if and only if A is type I. In 2008,
Kerr-Li-Pichot and, independently, Farah proved that when A is not type I,
then the irreducible representations are not even classifiable by
countable structures. I will show that a similar dichothomy holds for
classification of automorphisms up to unitary equivalence. Namely, the
automorphisms of a given separable unital C*-algebra A are classifiable by
real numbers if and only if A has continuous trace, and not even
classifiable by countable structures otherwise.