Mathematical Sciences: C*-Algebra Extensions and Homomorphisms

Lin将努力获得Weyl-von Neumann定理的扩展，该定理将用于给出C(X)的C*-代数扩展的完整分类，X是平面的紧子集，通过sigma单简单C*-代数。他还将研究是否每个实秩为零的C*-代数都有弱（FN），正如Lin在许多情况下所证明的那样。最后要研究的问题是从一个C*-代数到另一个C*-代数的同态等价类的分类问题。这个项目的一般数学领域在希尔伯特空间算子的代数理论中有其基础。运算符可以被认为是有限或无限的复数矩阵。特殊类型的运算符通常放在一个代数中，自然地称为运算符代数。这些抽象对象有各种各样的应用。例如，它们在结理论中发挥着关键作用，而结理论目前正被用于研究DNA的结构，它们在非交换几何中具有重要的基础意义，而非交换几何在物理学中正变得越来越重要。

Lin will work to obtain an extension of the Weyl-von Neumann theorem which will be used to give a complete classification of C*- algebra extensions of C(X), X a compact subset of the plane, by a sigma unital simple C*-algebra. He will also investigate whether every C*-algebra of real rank zero has weak (FN), as has been shown by Lin in many cases. A final problem to be studied is that of classifying certain equivalence classes of homomorphisms from one C*-algebra to another. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA, and they are of fundamental importance in non-commutative geometry, which is becoming increasingly important in physics.