量子群引论
Introduction to quantum groups
摘要：
这是对量子群的介绍，更确切地说，是对最简单的量子群的介绍。其思想是酉群$U_N$有一个自由的类似物$U_N^+$，其标准坐标$u_{ij}\in C(U_N^+)$可以是自由的，并且闭子群$G\subset U_N^+$可以被认为是紧量子李群。这样的量子群有许多有趣的例子，大多数是为了帮助解决量子力学和统计力学中的问题而设计的，还有一些通用的理论，包括彼得-外尔理论、塔纳基对偶、布劳尔定理和温加滕积分。我们在这里讨论这一切的基本方面。
英文摘要：
This is an introduction to the quantum groups, or rather to the simplest quantum groups. The idea is that the unitary group $U_N$ has a free analogue $U_N^+$, whose standard coordinates $u_{ij}\in C(U_N^+)$ are allowed to be free, and the closed subgroups $G\subset U_N^+$ can be thought of as being the compact quantum Lie groups. There are many interesting examples of such quantum groups, for the most designed in order to help with questions in quantum mechanics and statistical mechanics, and some general theory available as well, including Peter-Weyl theory, Tannakian duality, Brauer theorems and Weingarten integration. We discuss here the basic aspects of all this.
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。
