A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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

Volume 239 / 2017

Mahmood Alaghmandan, Jason Crann Studia Mathematica 239 (2017), 225-247 MSC: Primary 43A62; Secondary 43A20. DOI: 10.4064/sm8643-3-2017 Published online: 8 May 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.

Authors

  • Mahmood Alaghmandan
  • Jason Crann

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image