自由群因子在非素子因子和交换子代数上的不可分解性
Indecomposability of free group factors over nonprime subfactors and abelian subalgebras
摘要：
我们使用由D. Voiculescu证明了如果单项式的次数有一个依赖于生成元个数的上界，则自由群因子不能分解为非素子因子或交换$*$ -子代数的元素中的非交换单项式的闭线性跨距.由此得到的自由群因子的超有限维数和阿贝尔维数的估计满足L. Ge和S. Popa（无穷多个生成器）。
英文摘要：
We use the free entropy defined by D. Voiculescu to prove that the free group factors can not be decomposed as closed linear spans of noncommutative monomials in elements of nonprime subfactors or abelian $*$-subalgebras, if the degrees of monomials have an upper bound depending on the number of generators. The resulting estimates for the hyperfinite and abelian dimensions of free group factors settle in the affirmative a conjecture of L. Ge and S. Popa (for infinitely many generators).
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