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.
Original language | English |
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Journal | Journal of Operator Theory |
Volume | 87 |
Issue number | 1 |
Pages (from-to) | 3-23 |
Number of pages | 21 |
ISSN | 0379-4024 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
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- injective envelope, intersection property, primeness, Reduced crossed product, reduced group C-algebra
Research areas
ID: 342609412