Fourier algebras of hypergroups and central algebras on compact (quantum) groups
Volume 239 / 2017
Abstract
This paper concerns the study of regular Fourier hypergroups 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 $\mathbb {G}$, and in particular establish a completely isometric isomorphism with the center of the quantum group algebra for compact $\mathbb {G}$ of Kac type.
