论文标题
有限的阿贝尔组的非晶状体不平等熵尺寸
A Inequality for Non-Microstates Free Entropy Dimension for Crossed Products by Finite Abelian Groups
论文作者
论文摘要
对于某些生成子因子对$ M \子集M \ rtimes g $，其中$ g $是有限的Abelian集团，我们证明其非晶状体自由熵维度之间的不平等是大致的不平等，类似于自由组有限索引子组的较小级别的公式。作为一个应用程序，我们在形式的$ m \ rtimes（\ mathbb {z}/2 \ mathbb {z}）^{\ oplus \ infty} $的形式（\ mathbb {z}/2 \ mathbb {z}/2 \ mathbb {z}/2 \ mathbb {z}/2 \ mathbb {z}/2 \ roplus \ infty} $中，我们给出了界限。
For certain generating sets of the subfactor pair $M\subset M\rtimes G$ where $G$ is a finite abelian group we prove an approximate inequality between their non-microstates free entropy dimension, resembling the Shreier formula for ranks of finite index subgroups of free groups. As an application, we give bounds on free entropy dimension of generating sets of crossed products of the form $M\rtimes(\mathbb{Z}/2\mathbb{Z})^{\oplus\infty}$ for a large class of algebras $M$.
