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.

普渡大学研究基金会 研究人员将继续他的工作埃利奥特的程序分类简单或真实的秩零核C*-代数的K-理论和tracial不变量。 这将涉及研究发展一个本地理论的核C*-代数的近似乘法完全正映射的代数不变量的基础上有序模p K-理论。 在一个相关的方向调查将追求简单或真实的秩零次齐次C*-代数的局部谱可能有任意的维度增长的分类。他将研究分类结果在动力学中的应用。 C*-代数可以被认为是复数的无限矩阵的集合 显示丰富代数结构的数字。 它们对应于一种新的空间概念：非对易空间或量子空间。 在数学和物理的各个领域中，许多奇异空间都可以成功地用非交换C*-代数来代替。 值得注意的是，测度论、拓扑学、动力学和微分几何中的许多工具都对这种非交换环境进行了强大的扩展。