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Search: MSC category 46L37 ( Subfactors and their classification )

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1. CMB 2016 (vol 59 pp. 320)

Ino, Shoji
 Perturbations of Von Neumann Subalgebras with Finite Index In this paper, we study uniform perturbations of von Neumann subalgebras of a von Neumann algebra. Let $M$ and $N$ be von Neumann subalgebras of a von Neumann algebra with finite probabilistic index in the sense of Pimsner-Popa. If $M$ and $N$ are sufficiently close, then $M$ and $N$ are unitarily equivalent. The implementing unitary can be chosen as being close to the identity. Keywords:von Neumann algebras, perturbationsCategories:46L10, 46L37

2. CMB 2008 (vol 51 pp. 321)

Asaeda, Marta
 Quantum Multiple Construction of Subfactors We construct the quantum $s$-tuple subfactors for an AFD II$_{1}$ subfactor with finite index and depth, for an arbitrary natural number $s$. This is a generalization of the quantum multiple subfactors by Erlijman and Wenzl, which in turn generalized the quantum double construction of a subfactor for the case that the original subfactor gives rise to a braided tensor category. In this paper we give a multiple construction for a subfactor with a weaker condition than braidedness of the bimodule system. Categories:46L37, 81T05

3. CMB 2003 (vol 46 pp. 419)

Masuda, Toshihiko
 On Non-Strongly Free Automorphisms of Subfactors of Type III$_0$ We determine when an automorphism of a subfactor of type III$_0$ with finite index is non-strongly free in the sense of C.~Winsl\o w in terms of the modular endomorphisms introduced by M.~Izumi. Category:46L37

4. CMB 2003 (vol 46 pp. 80)

Erlijman, Juliana
 Multi-Sided Braid Type Subfactors, II We show that the multi-sided inclusion $R^{\otimes l} \subset R$ of braid-type subfactors of the hyperfinite II$_1$ factor $R$, introduced in {\it Multi-sided braid type subfactors} [E3], contains a sequence of intermediate subfactors: $R^{\otimes l} \subset R^{\otimes l-1} \subset \cdots \subset R^{\otimes 2} \subset R$. That is, every $t$-sided subfactor is an intermediate subfactor for the inclusion $R^{\otimes l} \subset R$, for $2\leq t\leq l$. Moreover, we also show that if $t>m$ then $R^{\otimes t} \subset R^{\otimes m}$ is conjugate to $R^{\otimes t-m+1} \subset R$. Thus, if the braid representation considered is associated to one of the classical Lie algebras then the asymptotic inclusions for the Jones-Wenzl subfactors are intermediate subfactors. Category:46L37

5. CMB 1997 (vol 40 pp. 254)

Saito, Kichi-Suke; Watatani, Yasuo
 Subdiagonal algebras for subfactors II (finite dimensional case) We show that finite dimensional subfactors do not have subdiagonal algebras unless the Jones index is one. Categories:46K50, 46L37
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