Mathematical Sciences: Operator Algebras and Noncommutative Topology

Blackadar教授将继续他关于算子代数结构和非交换代数拓扑的广泛问题的工作。具体的研究内容有：(I)齐次C~*-代数的归纳极限的结构；(Ii)非稳定K-理论与基本比较问题；(Iii)C~*-代数上上同调理论的存在性与性质。C*代数的概念是空间上的一族线性变换的概念的抽象。这些变换也可以被认为在空间的状态中具有值，而负责符号*的这个族的性质是，代数是由在这些状态中的值为实数的变换生成的。这些物体自然而然地出现在数学和物理的许多分支中，这使得研究它们变得重要。

Professor Blackadar will continue his work on a wide range of problems concerning the structure of operator algebras and noncommutative algebraic topology. Specific topics to be studied are: (i) structure of inductive limits of homogeneous C*- algebras, (ii) nonstable K-theory and the fundamental comparability question, and (iii) existence and properties of cohomology theories on C*-algebras. The notion of a C* algebra is an abstraction of the idea of a family of linear transformations on a space. These transformations can also be thought of as having values in the states of the space, and the property of this family which is responsible for the symbol * is that the algebra is generated by transformations whose values in these states are real numbers. The fact that these objects appear naturally in many branches of mathematics and physics make them important to study.