Constructing 2-cocycles on Fourier algebras
Yemon Choi (Lancaster University)
Thursday 31st January 16:00-17:00 Maths 311B
Recent progress in constructing derivations on Fourier algebras of connected Lie groups opens up the possibility of studying the spaces of higher-degree alternating cocycles on such algebras; these spaces ought to be related in some way to the Lie algebras of the respective groups, but the precise relationship is currently very far from understood. I will report on recent work in the degree 2 case, where we provide the first examples (and many of them) of groups whose Fourier algebras support non-trivial alternating 2-cocycles. A crucial ingredient is an unexpected "twisted inclusion" between two operator space tensor products, which is bounded but not completely bounded.