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The approximation property for locally compact quantum groups

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The approximation property for locally compact quantum groups. / Daws, Matthew; Krajczok, Jacek; Voigt, Christian.
In: Advances in Mathematics, Vol. 438, 109452, 29.02.2024.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Daws, M, Krajczok, J & Voigt, C 2024, 'The approximation property for locally compact quantum groups', Advances in Mathematics, vol. 438, 109452. https://doi.org/10.48550/arXiv.2305.04894, https://doi.org/10.1016/j.aim.2023.109452

APA

Daws, M., Krajczok, J., & Voigt, C. (2024). The approximation property for locally compact quantum groups. Advances in Mathematics, 438, Article 109452. https://doi.org/10.48550/arXiv.2305.04894, https://doi.org/10.1016/j.aim.2023.109452

Vancouver

Daws M, Krajczok J, Voigt C. The approximation property for locally compact quantum groups. Advances in Mathematics. 2024 Feb 29;438:109452. Epub 2024 Jan 2. doi: 10.48550/arXiv.2305.04894, 10.1016/j.aim.2023.109452

Author

Daws, Matthew ; Krajczok, Jacek ; Voigt, Christian. / The approximation property for locally compact quantum groups. In: Advances in Mathematics. 2024 ; Vol. 438.

Bibtex

@article{46985501c0474abd8dd17a99ee95ea61,
title = "The approximation property for locally compact quantum groups",
abstract = "We study the Haagerup--Kraus approximation property for locally compact quantum groups, generalising and unifying previous work by Kraus--Ruan and Crann. Along the way we discuss how multipliers of quantum groups interact with the $\mathrm{C}^*$-algebraic theory of locally compact quantum groups. Severalinheritance properties of the approximation property are established in this setting, including passage to quantum subgroups, free products of discrete quantum groups, and duals of double crossed products. We also discuss a relation to the weak$^*$ operator approximation property. For discrete quantumgroups, we introduce a central variant of the approximation property, and relate this to a version of the approximation property for rigid $\mathrm{C}^*$-tensor categories, building on work of Arano--De Laat--Wahl.",
keywords = "Locally compact quantum groups, Approximation property",
author = "Matthew Daws and Jacek Krajczok and Christian Voigt",
year = "2024",
month = feb,
day = "29",
doi = "10.48550/arXiv.2305.04894",
language = "English",
volume = "438",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - The approximation property for locally compact quantum groups

AU - Daws, Matthew

AU - Krajczok, Jacek

AU - Voigt, Christian

PY - 2024/2/29

Y1 - 2024/2/29

N2 - We study the Haagerup--Kraus approximation property for locally compact quantum groups, generalising and unifying previous work by Kraus--Ruan and Crann. Along the way we discuss how multipliers of quantum groups interact with the $\mathrm{C}^*$-algebraic theory of locally compact quantum groups. Severalinheritance properties of the approximation property are established in this setting, including passage to quantum subgroups, free products of discrete quantum groups, and duals of double crossed products. We also discuss a relation to the weak$^*$ operator approximation property. For discrete quantumgroups, we introduce a central variant of the approximation property, and relate this to a version of the approximation property for rigid $\mathrm{C}^*$-tensor categories, building on work of Arano--De Laat--Wahl.

AB - We study the Haagerup--Kraus approximation property for locally compact quantum groups, generalising and unifying previous work by Kraus--Ruan and Crann. Along the way we discuss how multipliers of quantum groups interact with the $\mathrm{C}^*$-algebraic theory of locally compact quantum groups. Severalinheritance properties of the approximation property are established in this setting, including passage to quantum subgroups, free products of discrete quantum groups, and duals of double crossed products. We also discuss a relation to the weak$^*$ operator approximation property. For discrete quantumgroups, we introduce a central variant of the approximation property, and relate this to a version of the approximation property for rigid $\mathrm{C}^*$-tensor categories, building on work of Arano--De Laat--Wahl.

KW - Locally compact quantum groups

KW - Approximation property

U2 - 10.48550/arXiv.2305.04894

DO - 10.48550/arXiv.2305.04894

M3 - Journal article

VL - 438

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 109452

ER -