Mathematical Sciences: Infinite Simple C*-Algebras and TheirInvariants

数学科学：无限简单 C* 代数及其不变量

• 批准号: 9626592
• 负责人: Shuang Zhang
• 金额: --
• 依托单位: University of Cincinnati Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626592&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Infinite; Simple; Algebras

DMS-9626592 PI: Shuang Zhang Univ of Cincinnati During the next three years the Principal Investigator, Shuang Zhang, proposes to continue his research on the following three problems. (1) Is there a simple C*-algebra that contains both finite and infinite nonzero projections? (2) Determine the K-theory of the simple C*-algebras generated by the reduced group C*-algebras associated with free products of cyclic groups and certain projections, and simple C*-algebras generated by a weighted bilateral shift and an isometry. (3) Classifying these non-nuclear, purely infinite, simple C*-algebras up to isomorphism. The problem (1) is an outstanding problem in the theory of simple C*-algebras and the program of classifying separable simple C*-algebras. The proposer intends to attack this problem by some techniques in the associated multiplier algebras. The C*-algebras in (2) and (3) include non-nuclear, purely infinite, simple C*-algebras which might serve as standard models in certain classes of non-nuclear simple C*-algebras. Investigation on the structure of these C*-algebras will supplement the expansion of classification program to the category of non-nuclear simple C*-algebras. Encouraged by the interests of several leading researchers on the projects above, the proposer expects that this investigation will stimulate fruitful research activities on the subjects. The collection of all linear transformations in the three dimensional space, and in any finite dimensional space, is generated by translations and certain rotations (via addition, scalar multiplication, and composition). This collection is the basic example of simple C*-algebras and can be identified with the algebra of all square matrices. These elementary simple C*-algebras are fully classified by the dimension of the space. Many problems in the quantum physics and in modern technologies (for example, computer programming) are reduced to the investigation of simple C*-algebras of this sort, and more generally, a variety of simple C*-algebras generated by certain linear transformations in the infinite dimensional space. The proposed project is concerned with the structure of simple C*-algebras generated by some square matrices of infinite size. In the process of increasing knowledge about these simple C*-algebras, one important step is to understand their structure and then to classify them. The proposed project is especially concerned with studying invariants that distinguish these algebras. The classical dimension is no longer the distinguishing invariant, and thus, finding and studying new distinguishing invariants become two key problems. The proposed project aims at attacking these outstanding problems in this area.

DMS-9626592 PI：张爽 辛辛那提大学 在接下来的三年里，首席研究员， 张爽建议继续研究以下问题 三个问题。(1)是否存在一个简单的C*-代数， 有限和无限非零投影(2)确定 约化群生成的单C ~*-代数的K-理论 与循环群的自由积有关的C ~*-代数及 某些投影，和简单的C*-代数产生的一个 加权双侧移位和等距。(3)对这些进行分类 非核的、纯无限的、直到同构的简单C*-代数。 问题（1）是简单理论中的一个突出问题 C ~*-代数与可分单分类程序 C*-代数提议者打算用一些方法来解决这个问题。 相关乘子代数中的技巧。C*-代数 在（2）和（3）中包括无核、纯无限、简单 C*-代数，可以作为标准模型在某些 非核单C*-代数类。 调查 这些C*-代数的结构将补充 分类程序的类别非核简单 C*-代数 在几个主要利益集团的鼓励下， 上述项目的研究人员，提案人预计， 这项调查将促进富有成果的研究活动 关于这些问题。 所有线性变换的集合 在任何有限维空间中， 通过平移和某些旋转（通过加法、标量 乘法和合成）。这个系列是基本的 一个简单的C*-代数的例子，并且可以与所有的代数等同起来。 方阵这些初等单C*-代数是完全的 按空间的维度分类。 诸多问题 量子物理学和现代技术（例如，计算机 程序设计）被简化为对简单C*-代数的研究 更一般地，各种简单C*-代数 由无限维空间中的某些线性变换产生 空间 拟议的项目涉及的结构 由无穷方阵生成的单C ~*-代数 尺寸在增加对这些简单的 对于C*-代数，重要的一步是了解它们的结构 然后将它们分类。该项目特别是 专注于研究区分这些代数的不变量。 经典维数不再是可区别的不变量， 从而发现和研究新的可区分不变量 成为两个关键问题。拟议的项目旨在解决这一领域的这些悬而未决的问题。