Strong Pedersen rigidity for coactions of compact groups

TL;DR

This paper establishes a strong form of Pedersen rigidity for coactions of compact groups, linking outer conjugacy of coactions to properties of dual actions and demonstrating a category equivalence.

Contribution

It proves a version of Pedersen's outer conjugacy theorem for compact group coactions, introducing the concept of strong Pedersen rigidity and establishing a category equivalence.

Findings

Every isomorphism of a dual action arises from a unique outer conjugacy of a coaction.

The paper characterizes outer conjugate coactions via dual action properties.

Introduces the concept of strong Pedersen rigidity for compact group coactions.

Abstract

We prove a version of Pedersen's outer conjugacy theorem for coactions of compact groups, which characterizes outer conjugate coactions of a compact group in terms of properties of the dual actions. In fact, we show that every isomorphism of a dual action comes from a unique outer conjugacy of a coaction, which in this context should be called strong Pedersen rigidity. We promote this to a category equivalence.