Mathematical Sciences: Inductive Limit C*-Algebras: Classification and Nonstable K-Theory

9401515帕斯尼库提出的研究有两个主要目的：1.根据其分次有序标度群对所有实秩零(稳定秩一)AH代数进行分类。2.得到AH-代数的非稳定K-理论结果。第一个项目的完成将是可分核C*-代数不变量分类问题的重要一步。第二个项目的完成将肯定地回答Blackadar的一个重要猜想，并将提供关于核C*-代数分类的重要信息。运算符是具有自然加法和乘法的矩阵的无限维广义。有一种自然对合，称为运算符的伴随运算，其行为非常类似于方阵上的转置运算(在对角线上的反射)。在加法、乘法、伴随运算下闭且具有一定拓扑性质的算子的集合称为C*-代数。这些代数在数学的几个分支以及数学物理和动力系统理论中都很重要。这里研究的C*-代数是以限制的方式由矩阵代数构成的C*-代数。基本目标是使用简单的不变量对这些重要的代数进行分类。***

9401515 Pasnicu The proposed research has two major objectives: 1.To classify all the real rank zero (stable rank one) AH algebras by their graded ordered scaled group. 2. To obtain nonstable K-theory results for AH algebras. The completion of the first project would be a major step in the classification problem of separable nuclear C*-algebras by invariants. The completion of the second project will give a positive answer to an important conjecture of Blackadar and will provide important information in itself and also concerning the classification of nuclear C*-algebras. Operators are infinite dimensional generalizations of matrices that possess a natural addition and multiplication. There is a natural involution called the adjoint operation on operators that behaves much like the transpose operation (reflection in the diagonal) on square matrices. A collection of operators that is closed under addition, multiplication, the adjoint operation and has a certain topological property is called a C*-algebra. These algebras are important in several branches of mathematics as well as in mathematical physics and dynamical systems theory. The C*-algebras investigated here are ones that are built out of matrix algebras in a limiting manner. The basic goal is to classify these important algebras using simple invariants. ***