本项目从两个方向研究有限von Neumann代数的相对顺从性。一是相对顺从性的等价刻画，本项目从新的视角，即自同构群的角度去研究。二是相对顺从性上的遗传问题，即假定一组有限von Neumann代数包含关系是顺从的，如果小代数具有某种性质，那么大代数是否也具有这种性质，本项目将考察von Neumann代数上的一个重要性质（McDuff性质）在相对顺从性上的遗传性。具体研究内容如下：（1）尝试用Alain Connes的自同构群技巧研究Sorin Popa在1986年提出的相对顺从性的自同构群角度的刻画问题。（2）研究相对顺从性的其它等价刻画，具体地，将injective operator system这一刻画推广到相对顺从性上。（3）重点考察McDuff性质的correspondence语言刻画并研究II1型因子的McDuff性质在相对顺从性的遗传性。

We will study relative amenability on finite von Neumann algebras from two directions. One is the new characterization of relative amenability using automorphisms, the other one is the study of permanent properties for amenable inclusions, i.e. what properties of the smaller subalgebra are inherited by the ambient algebra when the inclusion of finite von Neumann algebras is amenable. Specifically, this project aims at investigating the following three problems. First, we will use Alain Connes' automorphism machinery to study a problem on the equivalent characterizations of relative amenability on finite von Neumann algebras asked by Sorin Popa in 1986. Second, we will give one more characterization of relative amenability which can be thought of as an analogue of injective operator systems. Third, we will focus on the characterization of McDuff property using correspondence language and study the permanence of McDuff property under amenable inclusions of type II_1 factors.