The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

本文将阐明作者新近得到的C*-代数（C*-algebra）框架下局部紧量子群（locally compact quantum group）的简洁定义。与此同时，我们将该定义置于局部紧群、紧量子群（compact quantum groups）、Kac代数（Kac algebras）、乘法酉算子（multiplicative unitaries）以及对偶理论的历史与数学语境中进行梳理。