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

[401515] Pasnicu提议的研究有两个主要目标：1。将所有实秩0（稳定秩1）AH代数按它们的分级有序标度群进行分类。2. 得到AH代数的非稳定k理论结果。第一个课题的完成将是研究可分核C*-代数不变量分类问题的重要一步。第二个项目的完成将对Blackadar的一个重要猜想给出一个肯定的答案，并将提供关于核C*-代数分类的重要信息。算子是具有自然加法和乘法的矩阵的无限维推广。有一种自然对合称为算子的伴随运算，它的行为很像方阵上的转置运算（对角线上的反射）。对加法、乘法、伴随运算封闭并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*代数是由矩阵代数以一种极限的方式建立起来的。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. ***