Fourier algebras of hypergroups and central algebras on compact (quantum) groups

• © Instytut Matematyczny PAN, 2017. This paper concerns the study of regular Fourier hyper groups through multipliers of their associated Fourier algebras. We establish hypergroup analogues of well-known characterizations of group amenability, introduce a notion of weak amenability for hypergroups, and show that every discrete commutative hypergroup is weakly amenable with constant 1. Using similar techniques, we provide a sufficient condition for amenability of hypergroup Fourier algebras, which, as an immediate application, answers one direction of a conjecture of Azimifard-Samei-Spronk (2009) on the amenability of ZL 1 (G) for compact groups G. In the final section we consider Fourier algebras of hypergroups arising from compact quantum groups G, and in particular establish a completely isometric isomorphism with the center of the quantum group algebra for compact G of Kac type.

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NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

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