本项目将主要研究拓扑自由熵维数和C*-代数融合自由积。.拓扑自由熵维数是由D. Voiculescu引入的， D. Hadwin和沈隽浩对其进行了研究，得到一些比较深刻结果。已知能够使拓扑自由熵维数良定义的代数为MF代数。本项目计划在前人研究基础上，从影响拓扑自由熵维数的迹（trace）出发，研究一类特殊的代数理想，使得对某一类C*-代数的拓扑自由熵维数有了新的探讨途径。这类代数包括所有的nuclear MF代数。 .C*-代数融合自由积是群自由积在算子代数中的自然推广。由于其结构复杂，因此研究结果相对较少。关于融合自由积的一个重要问题是研究C*-代数融合自由积类型，本项目将致力于研究nuclear C*-代数和exact C*-代数的融合自由积。

In this project we mainly consider the topological free entropy dimension and unital amalgamated free products of C*-algebras.. The concept of topological free entropy dimension was given by D. Voiculescu. D. Hadwin and J. Shen have obtained many deep results in this field. Base on this research background, we are going to make furhter progress about it. From the previous research given by D. Hadwin and J. Shen, we know that the algebras which make the definition of topological free entropy dimension well defined are MF algebras. With the properties of some special traces, we are going to analyze these traces so that a particular type of ideal in MF algebras becomes important. Therefore it is capable of giving analysis of topological free entropy dimension for a type of C*-algebras which contains all nuclear MF algebras. . Unital amalgamated free products of C*-algebras is a generalization of amalagmated free products of groups. Since its construction is very complicated, less is known about it. One of the main problems in this field is to decide the tpye of an amalgamated free product of C*-algebras. In this project, we will analyze the types of unital amalgamated free products of nuclear C*-algebras and exact C*-algebras.