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

Mahmood Alaghmandan¹ ; Jason Crann¹

¹

Studia Mathematica, Tome 239 (2017) no. 3, pp. 225-247

Résumé

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.

Détail

DOI : 10.4064/sm8643-3-2017

Keywords: paper concerns study regular fourier hypergroups through multipliers their associated fourier algebras establish hypergroup analogues well known characterizations group amenability introduce notion weak amenability hypergroups every discrete commutative hypergroup weakly amenable constant using similar techniques provide sufficient condition amenability hypergroup fourier algebras which immediate application answers direction conjecture azimifard samei spronk amenability compact groups final section consider fourier algebras hypergroups arising compact quantum groups mathbb particular establish completely isometric isomorphism center quantum group algebra compact mathbb kac type