Realization of amenable bicategories and weak amenability of fusion algebras. (English) Zbl 0972.46043

Hayashi, Tomohiro

J. Math. Soc. Japan 53, No. 1, 147-174 (2001).

Summary: We consider the realization problem of amenable bicategories by using AFD-bimodules. As a corollary, we can realize an amenable standard lattice as that of an AFD \(\text{II}_1\)-subfactor. This gives another proof of S. Popa’s theorem. Weak amenability of fusion algebras is also discussed.

MSC:

46L37	Subfactors and their classification
46L08	\(C^*\)-modules

Keywords:

subfactor; realization problem of amenable bicategories; AFD-bimodules; fusion algebras