Mathematical Sciences: Invariants of C*-Algebras

达达尔拉特普渡大学研究Fdn研究者将继续他的艾略特的项目分类简单或实秩零核C*-代数的k -理论和迹迹不变量。这将涉及到基于有序模p - k理论的具有代数不变量的核C*-代数的近似乘法完全正映射的局部理论的研究。在一个相关的方向，研究者将追求简单或实秩零次齐次C*-代数的分类，其局部谱可能具有任意维增长。他将研究分类结果在动力学中的应用。C*代数可以被认为是无限复数矩阵的集合，具有丰富的代数结构。它们对应于一种新的空间概念：非交换空间或量子空间。许多在数学和物理的各个领域中需要的奇异空间可以被非交换的C*-代数成功地取代。值得注意的是，测量论、拓扑学、动力学和微分几何中的许多工具都对这种非交换设置有强大的扩展。

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.