## Abstract

Let G be a locally compact abelian group. By modifying a theorem of Pedersen, it follows that actions of G on C^{∗}-algebras A and B are outer conjugate if and only if there is an isomorphism of the crossed products that is equivariant for the dual actions and preserves the images of A and B in the multiplier algebras of the crossed products. The rigidity problem discussed in this paper deals with the necessity of the last condition concerning the images of A and B. There is an alternative formulation of the problem: an action of the dual group Ĝ together with a suitably equivariant unitary homomorphism of G give rise to a generalized fixed-point algebra via Landstad's theorem, and a problem related to the above is to produce an action of Ĝ and two such equivariant unitary homomorphisms of G that give distinct generalized fixed-point algebras. We present several situations where the condition on the images of A and B is redundant, and where having distinct generalized fixed-point algebras is impossible. For example, if G is discrete, this will be the case for all actions of G.

Original language | English (US) |
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Article number | 1850016 |

Journal | International Journal of Mathematics |

Volume | 29 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2018 |

## Keywords

- Action
- crossed-product
- exterior equivalence
- generalized fixed-point algebra
- outer conjugacy

## ASJC Scopus subject areas

- Mathematics(all)