**
Guy
Salomon,
Department
of
Pure
Mathematics,
University
of
Waterloo**

"Hyperrigid subsets of Cuntz–Krieger algebras and the property of rigidity at zero”

A
generating
set
of
a
C*-algebra is
said
to
be
*
hyperrigid*
if
for
every
faithful
nondegenerate
*-representation
of
the
C*-algebra
on
a
Hilbert
space
*
H*,
every
sequence
of
unital
completely
positive
self
maps
of
*
B(H)*
that
converges
to
the
identity
on
the
generating
set,
converges
to
the
identity
on
the
whole
C*-algebra
(all
convergences
are
in
the
pointwise-norm
sense).
I
will
show
that
inside
the
Cuntz–Krieger
algebra
of
a
row-finite
directed
graph
with
no
isolated
vertices,
the
set
of
all
edge
partial-isometries
is
hyperrigid.
I
will
also
present,
both
in
general
and
in
the
graph
context,
a
related
property
called
*
rigidity
at
zero*
that
sheds
light
on
the
phenomenon
of
hyperrigidity.

MC 5417