Yamagami, Shigeru Notes on amenability of commutative fusion algebras. (English) Zbl 0955.46027 Positivity 3, No. 4, 377-388 (1999). One of the prominent features of amenable fusion algebras is that the assumed dimension function is uniquely determined by the fusion algebra itself. It is proved by V. S. Sunder [Trans. Am. Math. Soc. 330, No. 1, 227-256 (1992; Zbl 0757.46053)] that there exists a unique dimension function for finite dimensional fusion algebras. The basic result in the paper is the following Theorem. A commutative \(F^*\)-algebra is amenable if and only if the associated regular representation is bounded. Reviewer: Farruh Mukhamedov (Tashkent) Cited in 4 Documents MSC: 46L05 General theory of \(C^*\)-algebras 46N50 Applications of functional analysis in quantum physics 46L55 Noncommutative dynamical systems Keywords:amenable fusion algebras; commutative fusion algebra; hypergroup; dimension functions; commutative \(F^*\)-algebra; regular representation Citations:Zbl 0757.46053 PDFBibTeX XMLCite \textit{S. Yamagami}, Positivity 3, No. 4, 377--388 (1999; Zbl 0955.46027) Full Text: DOI