极大子因子

On Maximal Subfactors

若N是一个Ⅱ1型因子,G是一个有限群且在N上有一个真外作用α,则当G的阶是素数对,N是Ⅱ1型因子M=N(?)αG的极大子因子．另一方面,假设 N(?) M是Ⅱ1型因子的一个包含,M(?)M1是N(?)M的基本构造,[M:N]= p∈N是素数,N’∩ M=CI,N’∩M1是交换的,N,(?)M深度为2,则N是M的极大子因子．

If N is a factor of type Ⅱ1 and G is a finite group with a properly outer action a on N, then N is a maximal subfactor in N ×α G when G is of prime order. Conversely, suppose that N 真包含M is an inclusion of factors of type Ⅱ1 and M 真包含M1 is the basic construction for N真包含M. If [M ： N] = p is a prime number, N’∩ M= CI, N’∩M1 is abclian and N 真包含M is of depth 2, then N is a maximal subfactor of M.