Normal intermediate subfactors

Details Normal intermediate subfactors Normal intermediate subfactors

1996-10-16

arxiv.org/abs/funct-an/9610002v1

Mathematics

Operator Algebras

25 pages, amslatex, to appear in J. Math. Soc. Japan

Scientific paper

Let $N \subset M$ be an irreducible inclusion of type type II$_1$ factors with finite Jones index. We shall introduce the notion of normality for intermediate subfactors of the inclusion $N \subset M$. If the depth of $N \subset M$ is 2, then an intermediate subfactor $K$ for $N \subset M$ is normal in $ N \subset M$ if and only if the depths of $N \subset K$ and $K \subset M$ are both 2. In particular, if $M$ is the crossed product $N \rtimes G$ of a finite group $G$, then $K = N \rtimes H$ is normal in $N \subset M$ if and only if $H$ is a normal subgroup of $G$.

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