Constructing 2-cocycles on Fourier algebras

Yemon Choi (Lancaster University)

Thursday 31st January 16:00-17:00 Maths 311B

Abstract

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.

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