Aasaimani Thamizhazhagan, Department of Pure Mathematics, University of Waterloo
"On the structure of invertible elements in Fourier-Stieltjes algebras"
For a locally compact abelian group $G$, J.L. Taylor (1971) gave a complete characterization of invertible elements in its measure algebra $M(G)$ engaging semigroup theory and cohomological calculations. Via Fourier-Stieltjes transforms, this characterization can be done in the context of Fourier-Stieltjes algebras $B(G)$ of abelian $G$. Following the investigation begun in M.E. Walter's work (1975), we have established this latter characterization for Fourier-Stieltjes algebra $B(G)$ of certain class of locally compact groups in particular, many totally minimal groups and $ax+b$ group.