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

2016/06/19 by Mahmood Alaghmandan, Alaghmandan, Mahmood, Jason Crann +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1606.05964

openalex publication_date 2016/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns the study of regular Fourier hypergroups through\nmultipliers of their associated Fourier algebras. We establish hypergroup\nanalogues of well-known characterizations of group amenability, introduce a\nnotion of weak amenability for hypergroups, and show that every discrete\ncommutative hypergroup is weakly amenable with constant 1. Using similar\ntechniques, we provide a sufficient condition for amenability of hypergroup\nFourier algebras, which, as an immediate application, answers one direction of\na conjecture of Azimifard--Samei--Spronk [J. Funct. Anal. 256(5) 1544-1564,\n2009] on the amenability of ZL¹(G) for compact groups G. In the final\nsection we consider Fourier algebras of hypergroups arising from compact\nquantum groups mathbbG, and in particular, establish a completely\nisometric isomorphism with the center of the quantum group algebra for compact\n mathbbG of Kac type.\n

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• Weak amenability of Fourier algebras on compact groups
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