Generalized Longo-Rehren subfactors and alpha-induction

Details Generalized Longo-Rehren subfactors and alpha-induction Generalized Longo-Rehren subfactors and alpha-induction

2001-07-18

arxiv.org/abs/math/0107127v1

Commun. Math. Phys. 226 (2002) 269-287

Mathematics

Operator Algebras

Scientific paper

10.1007/s002200200608

We study the recent construction of subfactors by Rehren which generalizes the Longo-Rehren subfactors. We prove that if we apply this construction to a non-degenerately braided subfactor N subset M and alpha-induction, then the resulting subfactor is dual to the Longo-Rehren subfactor M tensor M^opp subset R arising from the entire system of irreducible endomorphisms of M resulting from alpha-induction. As a corollary, we solve a problem on existence of braiding raised by Rehren negatively. Furthermore, we generalize our previous study with Longo and Muger on multi-interval subfactors arising from a completely rational conformal net of factors on S^1 to a net of subfactors and show that the (generalized) Longo-Rehren subfactors and alpha-induction naturally appear in this context.

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