Benjamin Steinberg, City College of New York
"Groupoid algebras and C*-algebras"
Groupoid
C*-algebras
form
a
unifying
framework
for
a
number
of
classes
of
C*-algebras
including
commutative
ones,
group
C^*-algebras,
group
action
cross
products
and
Cuntz-Krieger,
or
graph,
C*-algebras.
Often
purely
algebraic
properties
of
these
algebras
can
be
understood
in
terms
of
the
groupoids,
e.g.,
simplicity,
Morita
equivalence,
the
primitive
ideal
structure.
Over
the
past
decade,
Leavitt
path
algebras
have
become
very
popular
objects
in
noncommutative
algebra.
They
are
discrete
analogues,
defined
over
any
base
commutative
ring,
of
graph
C*-algebras.
It
has
been
observed
by
many
authors
that
there
are
very
tight
analogies
between
Leavitt
path
algebras
and
graph
C*-algebras,
but
a
common
unifying
framework
was
lacking.
In
2009
I
introduced
a
purely
algebraic
analogue
of
groupoid
C*-algebras.
My
original
motivation
was
to
study
inverse
semigroup
algebras
but
in
the
back
of
my
mind
was
to
create
this
uniform
framework.
A
group
of
operator
theorists,
in
particular
Brown,
Sims
and
Orloff-Clark,
have
also
begun
working
on
groupoid
algebras.
There
are
now
results
describing
Morita
equivalence,
modules,
simplicity,
primitivity
and
semiprimitivity
of
groupoid
algebras
in
groupoid
terms.
May
of
the
commonalities
between
Leavitt
path
algebras
and
graph
C*-algebras
have
received
a
uniform
explanation.
But
there
are
many
other
interesting
classes
of
groupoid
C*-algebras
whose
discrete
analogues
remain
to
be
explored.
Please note room - MC 4060.
Refreshments will be served in MC 5158B at 3:30pm.
All are welcome!