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

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.

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