On graded C*-algebras

TL;DR

This paper demonstrates that any topological grading of a C*-algebra by a discrete abelian group can be realized through an action of its dual compact group, linking gradings to group actions.

Contribution

It establishes a general correspondence between topological gradings and dual group actions for C*-algebras with abelian group gradings.

Findings

Every topological grading is implemented by a dual group action.

The result applies to all gradings by discrete abelian groups.

Provides a unified framework connecting gradings and group actions.

Abstract

We show that every topological grading of a C*-algebra by a discrete abelian group is implemented by an action of the compact dual group.