Injective envelopes and the intersection property

Institut for Matematiske Fag

Injective envelopes and the intersection property

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

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

Harvard

Bryder, RS 2022, 'Injective envelopes and the intersection property', Journal of Operator Theory, bind 87, nr. 1, s. 3-23. https://doi.org/10.7900/jot.2017jul26.2343

APA

Bryder, R. S. (2022). Injective envelopes and the intersection property. Journal of Operator Theory, 87(1), 3-23. https://doi.org/10.7900/jot.2017jul26.2343

Vancouver

Bryder RS. Injective envelopes and the intersection property. Journal of Operator Theory. 2022;87(1):3-23. https://doi.org/10.7900/jot.2017jul26.2343

Author

Bryder, Rasmus Sylvester. / Injective envelopes and the intersection property. I: Journal of Operator Theory. 2022 ; Bind 87, Nr. 1. s. 3-23.

Bibtex

@article{86c61c60aa594e9991998befb5bad303,

title = "Injective envelopes and the intersection property",

abstract = "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.",

keywords = "injective envelope, intersection property, primeness, Reduced crossed product, reduced group C-algebra",

author = "Bryder, {Rasmus Sylvester}",

year = "2022",

doi = "10.7900/jot.2017jul26.2343",

language = "English",

volume = "87",

pages = "3--23",

journal = "Journal of Operator Theory",

issn = "0379-4024",

publisher = "Academia Romana Institutul de Matematica",

number = "1",

}

RIS

TY - JOUR

T1 - Injective envelopes and the intersection property

AU - Bryder, Rasmus Sylvester

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