Evgenios Kakariadis, Department of Pure Mathematics University of Waterloo
“Isomorphism Invariants for C*-dynamical systems”
Apart
from
the
strong
interest
of
the
non-selfadjoint
operator
algebra
community
on
dynamics,
additional
motivation
for
their
examination
comes
from
the
recent
number
theoretic
papers
of
Cornelissen
and
Marcolli
and
also
from
their
work
in
graph
theory.
In
these
papers
Cornelissen
and
Marcolli
make
essential
use
of
the
work
of
Davidson
and
Katsoulis
on
non-selfadjoint
operator
algebras
associated
with
multivariable
dynamics
of
commutative
C*-
algebras.
As
it
turns
out,
the
key
link
with
non-selfadjoint
operator
algebras
is
provided
by
the
concept
of
piecewise
conjugacy
and
the
fact
that
piecewise
conjugacy
is
an
invariant
for
isomorphisms
between
certain
operator
algebras
associated
with
C*-dynamical
systems.
In
general,
the
following
two
problems
are
open
for
arbitrary
C*-dynamical
systems:
(i)
Identify
a
complete
invariant
for
isomorphisms
between
operator
algebras
associated
with
C*-
dynamical
systems.
(ii)
Develop
a
notion
of
piecewise
conjugacy
for
multivariable
systems
that
is
an
isomorphism
invariant
between
the
associated
operator
algebras.
In
this
talk
we
will
discuss
recent
progress
on
these
problems
from:
[1]
K.R.
Davidson
and
E.T.A.
Kakariadis,
Conjugate
Dynamical
Systems
on
C*-algebras,
Int.
Math.
Res.
Not.,
to
appear.
[2]
E.T.A.
Kakariadis
and
E.G.
Katsoulis,
Isomorphism
Invariants
for
Multivariable
C*-Dynamics,
preprint
arXiv:
1210.6068.