Normalizers of Irreducible Subfactors
نویسندگان
چکیده
We consider normalizers of an irreducible inclusion N ⊆ M of II1 factors. In the infinite index setting an inclusion uNu∗ ⊆ N can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these normalizers of N in M to projections in the basic construction and show that every trace one projection in the relative commutant N ′ ∩ 〈M, eN 〉 is of the form ueNu for some unitary u ∈ M with uNu∗ ⊆ N . This enables us to identify the normalizers and the algebras they generate in several situations. In particular each normalizer of a tensor product of irreducible subfactors is a tensor product of normalizers modulo a unitary. We also examine normalizers of irreducible subfactors arising from subgroup–group inclusions H ⊆ G. Here the normalizers are the normalizing group elements modulo a unitary from L(H). We are also able to identify the finite trace L(H)-bimodules in `2(G) as double cosets which are also finite unions of left cosets. AMS Classification: 46L10, 46L37
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