Normalizers of irreducible subfactors

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:352

Article

Smith, Roger¹  White, Stuart²  Wiggins, Alan³ 

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] Univ Glasgow, Dept Math, Glasgow G12 8QW, Lanark, Scotland

[3] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

关键词: Normalizers;    Irreducible subfactors;    Infinite index subfactors;    Group-subgroup inclusions;    Tensor products;    Finite factors;   

DOI  :  10.1016/j.jmaa.2008.11.019

来源: Elsevier

【 摘 要 】

We consider normalizers of an infinite index irreducible inclusion N subset of M of II1 factors. Unlike the finite index setting, an inclusion uNu* subset of 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' boolean AND M, e(N)) is of the form u*e(N)u for some unitary u is an element of M with uNu* subset of 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 front subgroup-group inclusions H subset of 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. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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