Reduced Twisted Crossed Products over C*-Simple Groups

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Standard

Reduced Twisted Crossed Products over C*-Simple Groups. / Bryder, Rasmus Sylvester; Kennedy, Matthew.

In: International Mathematics Research Notices, Vol. 2018, No. 6, 01.03.2018, p. 1638–1655.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Bryder, RS & Kennedy, M 2018, 'Reduced Twisted Crossed Products over C*-Simple Groups', International Mathematics Research Notices, vol. 2018, no. 6, pp. 1638–1655. https://doi.org/10.1093/imrn/rnw296

APA

Bryder, R. S., & Kennedy, M. (2018). Reduced Twisted Crossed Products over C*-Simple Groups. International Mathematics Research Notices, 2018(6), 1638–1655. https://doi.org/10.1093/imrn/rnw296

Vancouver

Bryder RS, Kennedy M. Reduced Twisted Crossed Products over C*-Simple Groups. International Mathematics Research Notices. 2018 Mar 1;2018(6):1638–1655. https://doi.org/10.1093/imrn/rnw296

Author

Bryder, Rasmus Sylvester ; Kennedy, Matthew. / Reduced Twisted Crossed Products over C*-Simple Groups. In: International Mathematics Research Notices. 2018 ; Vol. 2018, No. 6. pp. 1638–1655.

Bibtex

@article{d6278ce3b40b4cbab219b5710f98b64c,
title = "Reduced Twisted Crossed Products over C*-Simple Groups",
abstract = "We consider reduced crossed products of twisted C*-dynamical systems over C*-simple groups. We prove there is a bijective correspondence between maximal ideals of the reduced crossed product and maximal invariant ideals of the underlying C*-algebra, and a bijective correspondence between tracial states on the reduced crossed product and invariant tracial states on the underlying C*-algebra. In particular, the reduced crossed product is simple if and only if the underlying C*-algebra has no proper non-trivial invariant ideals, and has a unique tracial state if and only if the underlying C*-algebra has a unique invariant tracial state. We further show that the reduced crossed product satisfies an averaging property analogous to Powers{\textquoteright} averaging property. The dynamical systems are not required to be exact, and our results are new even in the non-twisted case.",
author = "Bryder, {Rasmus Sylvester} and Matthew Kennedy",
year = "2018",
month = mar,
day = "1",
doi = "10.1093/imrn/rnw296",
language = "English",
volume = "2018",
pages = "1638–1655",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "6",

}

RIS

TY - JOUR

T1 - Reduced Twisted Crossed Products over C*-Simple Groups

AU - Bryder, Rasmus Sylvester

AU - Kennedy, Matthew

PY - 2018/3/1

Y1 - 2018/3/1

N2 - We consider reduced crossed products of twisted C*-dynamical systems over C*-simple groups. We prove there is a bijective correspondence between maximal ideals of the reduced crossed product and maximal invariant ideals of the underlying C*-algebra, and a bijective correspondence between tracial states on the reduced crossed product and invariant tracial states on the underlying C*-algebra. In particular, the reduced crossed product is simple if and only if the underlying C*-algebra has no proper non-trivial invariant ideals, and has a unique tracial state if and only if the underlying C*-algebra has a unique invariant tracial state. We further show that the reduced crossed product satisfies an averaging property analogous to Powers’ averaging property. The dynamical systems are not required to be exact, and our results are new even in the non-twisted case.

AB - We consider reduced crossed products of twisted C*-dynamical systems over C*-simple groups. We prove there is a bijective correspondence between maximal ideals of the reduced crossed product and maximal invariant ideals of the underlying C*-algebra, and a bijective correspondence between tracial states on the reduced crossed product and invariant tracial states on the underlying C*-algebra. In particular, the reduced crossed product is simple if and only if the underlying C*-algebra has no proper non-trivial invariant ideals, and has a unique tracial state if and only if the underlying C*-algebra has a unique invariant tracial state. We further show that the reduced crossed product satisfies an averaging property analogous to Powers’ averaging property. The dynamical systems are not required to be exact, and our results are new even in the non-twisted case.

U2 - 10.1093/imrn/rnw296

DO - 10.1093/imrn/rnw296

M3 - Journal article

VL - 2018

SP - 1638

EP - 1655

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 6

ER -

ID: 176439492