Injective envelopes and the intersection property
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Injective envelopes and the intersection property. / Bryder, Rasmus Sylvester.
I: Journal of Operator Theory, Bind 87, Nr. 1, 2022, s. 3-23.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Injective envelopes and the intersection property
AU - Bryder, Rasmus Sylvester
N1 - Publisher Copyright: © 2022 THETA. All Rights Reserved.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - injective envelope
KW - intersection property
KW - primeness
KW - Reduced crossed product
KW - reduced group C-algebra
U2 - 10.7900/jot.2017jul26.2343
DO - 10.7900/jot.2017jul26.2343
M3 - Journal article
AN - SCOPUS:85123871930
VL - 87
SP - 3
EP - 23
JO - Journal of Operator Theory
JF - Journal of Operator Theory
SN - 0379-4024
IS - 1
ER -
ID: 342609412