Normalizers of Irreducible Subfactors
| dc.creator | Smith, Roger R. | |
| dc.creator | White, Stuart A. | |
| dc.creator | Wiggins, Alan D. | |
| dc.date | 2007-05-01 | |
| dc.date.accessioned | 2026-07-07T07:59:04Z | |
| dc.date.available | 2026-07-07T07:59:04Z | |
| dc.description | We consider normalizers of an irreducible inclusion $N\subseteq M$ of $\mathrm{II}_1$ factors. In the infinite index setting an inclusion $uNu^*\subseteq N$ 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 $N'\cap < M,e_N>$ is of the form $u^*e_Nu$ for some unitary $u\in M$ with $uNu^*\subseteq N$. 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 $H\subseteq G$. 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 $\ell^2(G)$ as double cosets which are also finite unions of left cosets. | |
| dc.description | 33 Pages | |
| dc.identifier | https://arxiv.org/abs/0705.0183 | |
| dc.identifier | http://arxiv.org/abs/0705.0183 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128230 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L10; 46L37 | |
| dc.title | Normalizers of Irreducible Subfactors | |
| dc.type | text |