Mathematical Sciences: Invariants of C*-Algebras

数学科学：C*-代数的不变量

• 批准号: 9622434
• 负责人: Marius Dadarlat
• 金额: $ 6.06万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622434&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Invariants; Algebras

DMS-9622434 Dadarlat Purdue University Research Fdn The investigator will continue his work on Elliott's program of classifying simple or real rank zero nuclear C*-algebras by K-theoretical and tracial invariants. This will involve research directed toward developing a local theory of approximately multiplicative completely positive maps of nuclear C*-algebras with algebraic invariants based on ordered mod-p K-theory. In a related direction the investigator will pursue the classification of simple or real rank zero subhomogeneous C*-algebras whose local spectra may have arbitrary dimension growth. He will study applications of the classification results into dynamics. C*-algebras can be thought as collections of infinite matrices of complex numbers displaying a rich algebraic structure. They correspond to a new idea of space: non-commutative or quantum space. Many singular spaces that are needed in the various areas of mathematics and physics can be successfully replaced by non-commutative C*-algebras. Remarkably, many of the tools of measure theory, topology, dynamics and differential geometry have powerful extensions to this non-commutative setting.

DMS-9622434 DADARLAT PURDUE大学研究FDN研究人员将继续他对Elliott的工作计划，该计划旨在通过K理论和曲折的不变式对简单或实际等级的零核C* - 代数进行分类。 这将涉及针对发展基于有序mod-p K理论的代数不变的核C*代数的近似乘法完全正面图的局部理论的研究。 在相关的方向上，研究者将追求简单或真实等级零均质的C* - 代数的分类，其本地光谱可能具有任意维度的增长。他将研究分类结果在动态中的应用。 C* - 代数可以被认为是表现出丰富代数结构的复数矩阵的集合。 它们对应于一个新的空间概念：非交通或量子空间。 在数学和物理学的各个领域所需的许多奇异空间都可以成功替换为非共同的C* - 代数。 值得注意的是，许多测量理论，拓扑，动力学和差异几何的工具具有强大的扩展，以使这种非交通设置。