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Notes on amenability of commutative fusion algebras. (English) Zbl 0955.46027

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.

MSC:

46L05 General theory of \(C^*\)-algebras
46N50 Applications of functional analysis in quantum physics
46L55 Noncommutative dynamical systems

Citations:

Zbl 0757.46053
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