The Structure of Nuclear C*-Algebras

抽象线 该项目是研究核C*-代数，通过研究 它们的同态，同构类型和它们的不变量， C ~*-代数的扩张。连续映射 拓扑空间之间的关系是至关重要的， topology.作为它们的非交换对应物，同态 在C*-代数理论中具有重要意义。 该项目的一部分是确定何时两个 从一个有单位可分核C*-代数到另一个C*-代数同态是（稳定）近似酉的 相当于它始终是理论的中心， 判定两个C*-代数同构的C*-代数 并描述它们的不变量。该项目的另一部分 是对（单）核可分C ~*-代数进行分类 通过K理论。这两个部分密切相关， 涉及C*-代数的一般理论，KK-理论， 自同构理论，C*-代数扩张理论， 群表示以及代数拓扑。 工程、物理科学和社会科学中的许多重要问题都需要这些知识 线性代数（或矩阵代数）来解决它们。 线性代数中的许多问题，特别是渐近和 线性代数中的逼近问题是最好的描述 无限维线性代数中的一个。C ~*-代数的研究 是研究无限维线性代数的。然而 C ~*-代数的应用范围从线性代数、算子 理论，群表示，动力系统，模拟量子 场论和量子统计力学。发展 C*-代数的理论，以及为了 应用到其他领域，主要是要有一个 更好地理解C*-代数的结构。是 该项目的宏伟目标是确定 具有最少可能数据的C*-代数。

Abstract Lin The project is to study nuclear C*-algebras by studying their homomorphisms, isomorphic types and their invariants, and by studying extensions of C*-algebras. Continuous maps between topological spaces are of fundamental importance in topology. As their noncommutative counterparts, homomorphisms are of fundamental importance in the theory of C*-algebras. One part of the project is to determine when two homomorphisms from one unital separable nuclear C*-algebra to another C*-algebra are (stably) approximately unitarily equivalent. It is always in the center of the theory of C*-algebras to determine when two C*-algebras are isomorphic and to describe their invariants. Another part of the project is to classify (simple) nuclear separable C*-algebras via their K-theory. These two parts are closely related and both involve the general theory of C*-algebras, KK-theory, the theory of automorphisms, the C*-algebra extension theory, the group representations as well as algebraic topology. Many important and significant problems in engineering, the physical sciences, and social sciences require the knowledge of linear algebras (or matrix algebras) to solve them. Many problems in linear algebras, in particular asymptotic and approximation problems in linear algebras are best described in infinite dimensional linear algebras. The study of C*-algebras is the study of infinite dimensional linear algebras. However the applications of C*-algebras range from linear algebras, operator theory, group representations, dynamic systems, to model quantum field theory and quantum statistical mechanics. For the development of the theory of C*-algebras as well as for the purpose of applications to other areas, it is primarily important to have a better understanding of the structure of C*-algebras. It is the ambitious goal of this project to determine the structure of C*-algebras with fewest possible data.