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

Access to Document

10.1142/S0129167X23500830

Cite this

@article{fcaaed62d0cc4a3db441f98fdf15a49d,

title = "Strong Pedersen rigidity for coactions of compact groups",

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.",

keywords = "Action, coaction, generalized fixed-point algebra, outer conjugate",

author = "S. Kaliszewski and Tron Omland and John Quigg and Jonathan Turk",

note = "Publisher Copyright: {\textcopyright} 2023 World Scientific Publishing Company.",

year = "2023",

month = nov,

day = "1",

doi = "10.1142/S0129167X23500830",

language = "English (US)",

volume = "34",

journal = "International Journal of Mathematics",

issn = "0129-167X",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "13",

}

TY - JOUR

T1 - Strong Pedersen rigidity for coactions of compact groups

AU - Kaliszewski, S.

AU - Omland, Tron

AU - Quigg, John

AU - Turk, Jonathan

PY - 2023/11/1

Y1 - 2023/11/1

N2 - 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.

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.

KW - Action

KW - coaction

KW - generalized fixed-point algebra

KW - outer conjugate

UR - http://www.scopus.com/inward/record.url?scp=85173275376&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85173275376&partnerID=8YFLogxK

U2 - 10.1142/S0129167X23500830

DO - 10.1142/S0129167X23500830

M3 - Article

AN - SCOPUS:85173275376

SN - 0129-167X

VL - 34

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 13

M1 - 2350083

ER -

Strong Pedersen rigidity for coactions of compact groups

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this