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

数学科学：归纳极限 C* 代数：分类和不稳定 K 理论

• 批准号: 9401515
• 负责人: Cornel Pasnicu
• 金额: $ 5.76万
• 依托单位: University of Puerto Rico-Rio Piedras
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401515&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Inductive; Limit; Algebras

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. ***

小行星9401515 本文的研究有两个主要目标：1.利用分次序标度群对所有真实的秩零（稳定秩一）AH代数进行分类。2.获得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给出一个积极的答案的一个重要猜想的Blackadar，并将提供重要的信息本身，也有关分类的核C*-代数。 算子是矩阵的无限维推广，具有自然的加法和乘法。 有一种自然的对合称为算子上的伴随运算，其行为很像方阵上的转置运算（对角线上的反射）。一个在加法、乘法、伴随运算下闭的算子集合，并且具有一定的拓扑性质，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从矩阵代数中构建出来的。 基本目标是使用简单不变量对这些重要的代数进行分类。 ***