Dan Ursu, Pure Math Department, University of Waterloo
"Relative C*-Simplicity"
Groups
are
good
for
one
thing
and
that's
acting
on
things.
We
can
consider
the
action
of
a
group
G
on
a
C*-algebra
A,
and
just
like
for
the
semidirect
product
of
two
groups,
we
can
embed
G
and
A
into
a
larger
C*-algebra
where
the
action
is
inner.
This
forms
what's
called
a
crossed
product.
A
recent
result
of
Amrutam
gives
a
sufficient
condition
for
all
C*-subalgebras
of
a
crossed
product
that
contain
G
to
also
themselves
be
crossed
products
with
G.
Namely,
this
is
true
if
the
kernel
of
the
action
of
G
on
A
is
what
he
calls
plump.
Plumpness
is
a
relative
version
of
something
called
Power's
averaging
property,
which
is
known
to
being
equivalent
to
the
reduced
C*-algebra
of
G
being
simple
(i.e.
G
is
C*-simple).
With
this
in
mind,
and
with
the
intention
of
coming
up
with
a
better
name
than
plump,
we
come
up
with
the
notion
of
a
relatively
C*-simple
subgroup
of
G,
and
it
is
possible
to
show
that
these
two
notions
are
equivalent,
along
with
several
other
characterizations.
In
this
talk,
I
will
build
up
all
of
the
necessary
prerequisites,
and
give
a
brief
overview
of
the
equivalences
mentioned
earlier.
Finally,
with
this,
I
will
prove
some
easy
examples
of
relatively
C*-simple
subgroups.
MC
5403