Michael Hartz, Department of Pure Mathematics, University of Waterloo
"Universal operator algebras for commuting row contractions"
In
this
talk,
we
will
consider
universal
operator
algebras
generated
by
commuting
row
contractions
satisfying
homogeneous
polynomial
relations.
These
algebras
can
be
realized
as
algebras
of
functions
on
the
varieties
defined
by
the
relations.
It
turns
out
that
their
structure
is
closely
related
to
the
geometry
of
the
associated
algebraic
varieties.
We
will
discuss
the
question
of
when
two
algebras
of
this
are
type
isomorphic.
In
particular,
we
will
see
that
two
such
algebras
are
topologically
isomorphic
if
and
only
if
there
is
an
invertible
linear
map
on
Cd
which
maps
one
variety
isometrically
onto
the
other.
This
builds
on
the
theory
developed
by
Davidson,
Ramsey
and
Shalit.
The
main
new
ingredient
is
to
show
that
finite
algebraic
sums
of
full
Fock
spaces
over
subspaces
of
Cd
are
closed.