Derivations on Fourier algebras of connected Lie groups
Yemon Choi (Lancaster University)
Tuesday 6th May, 2014 16:00-17:00 Maths 416
A long-running theme in the study of Banach algebras concerns the existence or otherwise of non-zero derivations from various Banach function algebras into natural coefficient modules. One class of examples which have not been studied so extensively are the Fourier algebras of connected groups. Work of B. E. Johnson (1994) shows that derivations into the dual of the algebra exist for all compact non-abelian Lie groups, but since then there has been something of an impasse. In this talk, after giving some of the background, I will discuss Johnson's result from a slightly different perspective, explaining how one can reinterpret his proof as an application of orthogonality relations for coefficient functions. Then I will present some recent joint work with M. Ghandehari where we are able to apply this idea to handle new classes of non-compact groups. If time permits I will say something about even more recent work on the Heisenberg group.