Rigidity theory for C∗-dynamical systems and the “Pedersen Rigidity Problem”, II

Author:

Kaliszewski S.1,Omland Tron23,Quigg John1ORCID

Affiliation:

1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, USA

2. Department of Mathematics, University of Oslo, NO-0316 Oslo, Norway

3. Department of Computer Science, Oslo Metropolitan University, NO-0130 Oslo, Norway

Abstract

This is a follow-up to a paper with the same title and by the same authors. In that paper, all groups were assumed to be abelian, and we are now aiming to generalize the results to nonabelian groups. The motivating point is Pedersen’s theorem, which does hold for an arbitrary locally compact group [Formula: see text], saying that two actions [Formula: see text] and [Formula: see text] of [Formula: see text] are outer conjugate if and only if the dual coactions [Formula: see text] and [Formula: see text] of [Formula: see text] are conjugate via an isomorphism that maps the image of [Formula: see text] onto the image of [Formula: see text] (inside the multiplier algebras of the respective crossed products). We do not know of any examples of a pair of non-outer-conjugate actions such that their dual coactions are conjugate, and our interest is therefore exploring the necessity of latter condition involving the images; and we have decided to use the term “Pedersen rigid” for cases where this condition is indeed redundant. There is also a related problem, concerning the possibility of a so-called equivariant coaction having a unique generalized fixed-point algebra, that we call “fixed-point rigidity”. In particular, if the dual coaction of an action is fixed-point rigid, then the action itself is Pedersen rigid, and no example of non-fixed-point-rigid coaction is known.

Funder

Research Council of Norway through FRINATEK

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Strong Pedersen rigidity for coactions of compact groups;International Journal of Mathematics;2023-09-29

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