Injective envelopes and the intersection property
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We consider the ideal structure of a reduced crossed product of a unital C* -algebra equipped with an action of a discrete group. More specifically we find sufficient and necessary conditions for the group action to have the intersection property, meaning that non-zero ideals in the reduced crossed product restrict to non-zero ideals in the underlying C*-algebra. We show that the intersection property of a group action on a C*-algebra is equivalent to the intersection property of the action on the equivariant injective envelope. We also show that the centre of the equivariant injective envelope always contains a C*-algebraic copy of the equivariant injective envelope of the centre of the injective envelope. Finally, we give applications of these results in the case when the group is C*-simple.
Originalsprog | Engelsk |
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Tidsskrift | Journal of Operator Theory |
Vol/bind | 87 |
Udgave nummer | 1 |
Sider (fra-til) | 3-23 |
Antal sider | 21 |
ISSN | 0379-4024 |
DOI | |
Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
Acknowledgements. The author is supported by a Ph.D. stipend from the Danish National Research Foundation (DNRF) through the Centre for Symmetry and Deformation at University of Copenhagen. The author is grateful to Magdalena Musat and Mikael Rørdam for their invaluable suggestions and comments, as well as their support.
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