In the paper, we apply the notion of local group in the context of operator algebras, and propose C*-algebraic constructions related to local groups. For a local group we define the concepts of *-representation and strong *-representation which are related to each other with the help of the extension of the local group. The structure of local group allows us to define the regular representation, which is a *-representation, and the respective reduced C*-algebra; the latter is graded over the extension of the local group.

中文翻译：

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地方团体及其代表

在本文中，我们在算子代数的上下文中应用局部群的概念，并提出与局部群有关的C *代数构造。对于本地组，我们定义了*表示和强*表示的概念，这些概念在本地组的扩展帮助下彼此相关。局部群的结构使我们能够定义正则表示（即*表示）以及相应的归约C *代数；后者根据本地群体的扩展等级。