Mathematical Sciences: Operator Algebras and Noncommutative Topology

Blackadar教授将继续研究有关算子代数结构和非交换代数拓扑的广泛问题。具体研究的课题有：(i)齐次C*-代数的归纳极限结构；（ii）非稳定k理论与基本可比性问题；（iii） C*-代数上同调理论的存在性与性质。C*代数的概念是对空间上一系列线性变换的抽象。这些变换也可以被认为是在空间的状态中有值，这个族的性质是负责符号*的是代数是由这些状态中的值是实数的变换生成的。这些对象在数学和物理的许多分支中自然出现的事实，使它们成为研究的重要对象。

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.