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.