张量积的广群正规化子
Groupoid normalizers of tensor products
摘要：
考虑有限von Neumann代数的包含$B\subseteq M$满足$B'\cap M\subseteq B$ .偏等距$v\in M$称为广群正规化子，如果$vBv^*, v^*Bv\subseteq B$。给定两个这样的包含$B_i\subseteq M_i$，$i=1,2$，我们在$M_1\vnotimes M_2$中找到了$B_1 \vnotimes B_2$的群胚正规化子的近似，由此我们推出了由张量积的群胚正规化子生成的von Neumann代数等于由群胚正规化子生成的von Neumann代数的张量积.给出的例子表明，这可能会失败，没有假设$B_i'\cap M_i\subseteq B_i$，$i=1,2$。我们还证明了一个平行的结果，其中的群正规化取代的交织，这些部分等距$v\in M$满足$vBv^*\subseteq B$和$v^*v, vv^*\in B$。
英文摘要：
We consider an inclusion $B\subseteq M$ of finite von Neumann algebras satisfying $B'\cap M\subseteq B$. A partial isometry $v\in M$ is called a groupoid normalizer if $vBv^*, v^*Bv\subseteq B$. Given two such inclusions $B_i\subseteq M_i$, $i=1,2$, we find approximations to the groupoid normalizers of $B_1 \vnotimes B_2$ in $M_1\vnotimes M_2$, from which we deduce that the von Neumann algebra generated by the groupoid normalizers of the tensor product is equal to the tensor product of the von Neumann algebras generated by the groupoid normalizers. Examples are given to show that this can fail without the hypothesis $B_i'\cap M_i\subseteq B_i$, $i=1,2$. We also prove a parallel result where the groupoid normalizers are replaced by the intertwiners, those partial isometries $v\in M$ satisfying $vBv^*\subseteq B$ and $v^*v, vv^*\in B$.
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