Event Details

Building 2-cocycles on Fourier algebras: how hard can it be?

Constructing non-trivial 1-cocycles (i.e. non-inner derivations) on various commutative Banach algebras, or proving that none exist, has been a well-known pastime. Constructing the degree 2 versions, or proving that none exist, seems to be less reputable or less explored. In this talk I will focus on the class of Fourier algebras of Lie groups, where these cocycles should reflect some of the structure in the underlying Lie groups, and explain why constructing 2-cocycles seems to be significantly harder than constructing 1-cocycles. I will then present some recent results showing that 2-cocycles can be constructed for a large number of Lie groups, although the case of SU(3) is still unknown. Depending on the time available and the audience, I may say something about unexpected technical ingredients required in this proof, including the newfangled ("operator space tensor products") and the classical (Riesz-Thorin interpolation).