Analysis seminar

Friday, March 1, 2013 3:30 pm - 3:30 pm EST (GMT -05:00)

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.