Normalizers of irreducible subfactors Academic Article uri icon

abstract

  • We consider normalizers of an infinite index irreducible inclusion N ⊆ M of II 1 factors. Unlike the finite index setting, an inclusion u N u * ⊆ N can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these one-sided normalizers of N in M to projections in the basic construction and show that every trace one projection in the relative commutant N ′ ∩ 〈 M, e N 〉 is of the form u * e N u for some unitary u ∈ M with u N u * ⊆ N generalizing the finite index situation considered by Pimsner and Popa. We use this to show that each normalizer of a tensor product of irreducible subfactors is a tensor product of normalizers modulo a unitary. We also examine normalizers of infinite index irreducible subfactors arising from subgroup-group inclusions H ⊆ G. Here the one-sided normalizers arise from appropriate group elements modulo a unitary from L (H). We are also able to identify the finite trace L (H)-bimodules in ℓ 2 (G) as double cosets which are also finite unions of left cosets. © 2008 Elsevier Inc. All rights reserved.

author list (cited authors)

  • Smith, R., White, S., & Wiggins, A.

citation count

  • 5

complete list of authors

  • Smith, Roger||White, Stuart||Wiggins, Alan

publication date

  • April 2009