We extend the Longo-Rehren construction to an infinite system of bimodules (of sectors). The construction is similar to the crossed product. We also show that the Longo-Rehren construction gives an isomorphic subfactor to Popa's symmetric enveloping algebra. We discuss the relation between the Longo-Rehren subfactors and amenability of fusion algebras in the sense of Hiai and Izumi.
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