
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.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Noncommutative and Quantum Gravity Theories
