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