# Mappings preserving cosets of subgroups and the Fourier-Stieltjes algebra

Michael Cowling
University of New South Wales, Sydney, Australia
22 Nov 2010 Noon-1pm, Carslaw Room 707A

## Abstract

I will outline two parallel families of results. Suppose that $$G_1$$ and $$G_2$$ are connected Lie groups, and that  $$\phi: G_1 \to G_2$$ is a bijection. In many cases it is possible to prove that, if $$\phi$$ sends cosets of subgroups to cosets of subgroups, or if composition with $$\phi$$  maps the Fourier-Stieltjes algebra $$B(G_2)$$ to $$B(G_1)$$, then $$\phi$$ is composed of some or all of the following: a group isomorphism; a translation, and reflection. Curiously, nilpotent Lie groups are the hardest to deal with.