非对易几何的思想和概念的非正式介绍
An informal introduction to the ideas and concepts of noncommutative geometry
摘要：
这个非正式的介绍是在第六届Peyresq会议"可积系统和量子场论“的三个小时的演讲的扩展版本。在这个演讲中，我们将概述一些数学结果，这些结果推动了所谓的非对易几何的发展。第一个这些结果是定理Gelfand和Neumark约交换$C^\ast$ -代数，然后来一些方面的$K$ -理论，首先为拓扑空间，然后为$C^\ast$ -代数，最后纯代数的版本。循环同调的介绍，记住它的关系，微分结构。最后的结果是陈省身性格的建构，它显示了这些发展是如何相互关联的。
英文摘要：
This informal introduction is an extended version of a three hours lecture given at the 6th Peyresq meeting ``Integrable systems and quantum field theory''. In this lecture, we make an overview of some of the mathematical results which motivated the development of what is called noncommutative geometry. The first of these results is the theorem by Gelfand and Neumark about commutative $C^\ast$-algebras; then come some aspects of the $K$-theories, first for topological spaces, then for $C^\ast$-algebras and finally the purely algebraic version. Cyclic homology is introduced, keeping in mind its relation to differential structures. The last result is the construction of the Chern character, which shows how these developments are related to each other.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
