Simple C*-Algebras and Dynamical Systems: Classification and Applications

************Abstract*****************************************The首席研究员龚桂华和李良清建议继续他们对可分、可服从C*-代数分类的研究。他们还计划研究在动力系统研究中自然产生的叉积C*-代数。所采用的方法包括KK理论、E理论、长度可控的同伦路径、谱切割和吸收。量子物理中从有限个自由度到无限个自由度的过渡导致了某些无限维代数的数学理论，称为C*-代数。C*-代数是一个代数系统，类似于数的代数系统，具有加法、减法、乘法和除法运算。但与数的乘法不同，C*-代数中的乘法是不可交换的-也就是说，一般而言，X乘以Y并不等于Y乘以X。这一重要特征对应于量子力学中的海森伯格测不准原理。研究人员建议对一大类可服从C*-代数进行完全计数(或分类)。他们预计，拟议研究的进展将在几个数学领域做出重要贡献，包括算子代数、微分拓扑学，以及对量子物理无限维世界的理解。

************Abstract*****************************************The principal investigators, Guihua Gong and Liangqing Li, propose to continue their research on the classification of separable, amenable C*-algebras. They also plan to study the cross product C*-algebras which arise naturally in the study of dynamical systems. The methods to be employed include KK-theory, E-theory, homotopy path with controlled length, and spectrum cutting and absorption.The passage from a finite to an infinite number of degrees of freedom in quantum physics led to the mathematical theory of certain infinite dimensional algebras, called C*-algebras. A C*-algebra is an algebraic system, similar to that of numbers, with its operations of addition, subtraction, multiplication, and division. But unlike the multiplication for numbers, the multiplication in a C*-algebra is not commutative ---- that is, in general, X times Y is not as same as Y times X. This important feature corresponds to Heisenberg uncertainty principle in Quantum Mechanics. The investigators propose to work on a complete enumeration (or classification) of a large class of amenable C*-algebras. They expect that progress on the proposed research will result in important contributions to several mathematical fields including operator algebras, differential topology, and also to the understanding of the infinite dimensional world of quantum physics.