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Commutativity of automorphisms
of subfactors modulo inner automorphisms

Author: Satoshi Goto
Journal: Proc. Amer. Math. Soc. 124 (1996), 3391-3398
MSC (1991): Primary 46L37
MathSciNet review: 1340387
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Abstract: We introduce a new algebraic invariant $\chi _{a}(M,N)$ of a subfactor $N \subset M$. We show that this is an abelian group and that if the subfactor is strongly amenable, then the group coincides with the relative Connes invariant $\chi (M,N)$ introduced by Y. Kawahigashi. We also show that this group is contained in the center of $ {\hbox {Out}}(M,N)$ in many interesting examples such as quantum $SU(n)_{k}$ subfactors with level $k$ $(k \geq n+1)$, but not always contained in the center. We also discuss its relation to the most general setting of the orbifold construction for subfactors.

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Additional Information

Satoshi Goto
Affiliation: Department of Mathematics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102, Japan

Keywords: Approximately inner automorphism, centrally trivial automorphism, Loi's invariant, non-strongly outer automorphism, orbifold construction, quantum $SU(n)_{k}$ subfactor, relative Connes invariant
Received by editor(s): March 9, 1995
Received by editor(s) in revised form: May 8, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society