群型子因子与Hadamard矩阵
Group-type subfactors and Hadamard matrices
摘要：
通过基本构造的迭代，可以从对称交换方获得超有限的$II_1$子因子。对于某些从阿达玛矩阵构造的交换平方，我们将这个子因子描述为群型包含$R^H \subset R \rtimes K$，其中$H$和$K$是在超有限$II_1$因子$R$上具有外部作用的有限群。我们找到了由$H$和$K$生成的外自同构群，并利用Bisch和Haagerup的方法确定了主图和对偶主图.在某些情况下，通过检查与动作相关的$H^3(H \ast K / Int R)$元素，可以获得完整的分类。
英文摘要：
A hyperfinite $II_1$ subfactor may be obtained from a symmetric commuting square via iteration of the basic construction. For certain commuting squares constructed from Hadamard matrices, we describe this subfactor as a group-type inclusion $R^H \subset R \rtimes K$, where $H$ and $K$ are finite groups with outer actions on the hyperfinite $II_1$ factor $R$. We find the group of outer automorphisms generated by $H$ and $K$, and use the method of Bisch and Haagerup to determine the principal and dual principal graphs. In some cases a complete classification is obtained by examining the element of $H^3(H \ast K / Int R)$ associated with the action.
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