Local Groups and Their Representations

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.