Elcim Elgun, Department of Pure Mathematics, University of Waterloo
"The Eberlein Compactication of the Heisenberg Type Group Z T T"
Given
a
locally
compact
group
G,
the
Eberlein
compactication
Ge
is
the
spectrum
of
the
uniform
closure
of
the
Fourier-Stieltjes
algebra
B(G).
It
is
a
semitopological
semigroup
compactication
and
thus
a
quotient
of
the
weakly
almost
periodic
compactication
of
G.
In
this
talk
we
aim
to
study
the
Eberlein
compactication
of
the
group
ZTT
equipped
with
Heisenberg
type
multiplication.
First,
we
will
see
that
transitivity
properties
of
the
action
of
ZT
on
the
central
subgroup
T
force
some
aspects
of
the
structure
of
(ZTT)e
to
be
quite
simple.
On
the
other
hand,
we
will
observe
that
the
Eberlein
compactication
of
the
direct
product
group
Z
T
is
large
with
a
complicated
structure,
and
can
be
realized
as
a
quotient
of
the
Eberlein
compactication
(Z
T
T)e.