Strong Pedersen rigidity for coactions of compact groups

S. Kaliszewski; Tron Omland; John Quigg; Jonathan Turk

doi:10.1142/S0129167X23500830

Strong Pedersen rigidity for coactions of compact groups

S. Kaliszewski, Tron Omland, John Quigg, Jonathan Turk

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	2350083
Journal	International Journal of Mathematics
Volume	34
Issue number	13
DOIs	https://doi.org/10.1142/S0129167X23500830
State	Published - Nov 1 2023

Keywords

Action
coaction
generalized fixed-point algebra
outer conjugate

ASJC Scopus subject areas

General Mathematics

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10.1142/S0129167X23500830

Cite this

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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.",

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AU - Turk, Jonathan

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AB - 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.

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KW - generalized fixed-point algebra

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Strong Pedersen rigidity for coactions of compact groups

Abstract

Keywords

ASJC Scopus subject areas

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