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Rights statement: This is the author’s version of a work that was accepted for publication in Advnces in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published inAdvances in Mathematics, 385, 2021 DOI: 10.1016/j.aim.2021.107747

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Constructing alternating 2-cocycles on Fourier algebras

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In: Advances in Mathematics, Vol. 385, 107747, 16.07.2021.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Author

Choi, Yemon. / Constructing alternating 2-cocycles on Fourier algebras. In: Advances in Mathematics. 2021 ; Vol. 385.

Bibtex

@article{a251fb1dd3414c65a20bafda567a4c2c,
title = "Constructing alternating 2-cocycles on Fourier algebras",
abstract = "Building on recent progress in constructing derivations on Fourier algebras, we provide the first examples of locally compact groups whose Fourier algebras support non-zero, alternating 2-cocycles; this is the first step in a larger project. Although such 2-cocycles can never be completely bounded, the operator space structure on the Fourier algebra plays a crucial role in our construction, as does the opposite operator space structure.Our construction has two main technical ingredients: we observe that certain estimates from [H. H. Lee, J. Ludwig, E. Samei, N. Spronk, Weak amenability of Fourier algebras and local synthesis of the anti-diagonal, Adv. Math., 292 (2016)] yield derivations that are {"}co-completely bounded{"} as maps from various Fourier algebras to their duals; and we establish a twisted inclusion result for certain operator space tensor products, which may be of independent interest. ",
keywords = "Alternating cocycle, Co-completely bounded, Fourier algebra, Hochschild cohomology, Opposite operator space, Tensor product",
author = "Yemon Choi",
note = "This is the author{\textquoteright}s version of a work that was accepted for publication in Advnces in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published inAdvances in Mathematics, 385, 2021 DOI: 10.1016/j.aim.2021.107747",
year = "2021",
month = jul,
day = "16",
doi = "10.1016/j.aim.2021.107747",
language = "English",
volume = "385",
issn = "0001-8708",

}

RIS

TY - JOUR

T1 - Constructing alternating 2-cocycles on Fourier algebras

AU - Choi, Yemon

N1 - This is the author’s version of a work that was accepted for publication in Advnces in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published inAdvances in Mathematics, 385, 2021 DOI: 10.1016/j.aim.2021.107747

PY - 2021/7/16

Y1 - 2021/7/16

N2 - Building on recent progress in constructing derivations on Fourier algebras, we provide the first examples of locally compact groups whose Fourier algebras support non-zero, alternating 2-cocycles; this is the first step in a larger project. Although such 2-cocycles can never be completely bounded, the operator space structure on the Fourier algebra plays a crucial role in our construction, as does the opposite operator space structure.Our construction has two main technical ingredients: we observe that certain estimates from [H. H. Lee, J. Ludwig, E. Samei, N. Spronk, Weak amenability of Fourier algebras and local synthesis of the anti-diagonal, Adv. Math., 292 (2016)] yield derivations that are "co-completely bounded" as maps from various Fourier algebras to their duals; and we establish a twisted inclusion result for certain operator space tensor products, which may be of independent interest.

AB - Building on recent progress in constructing derivations on Fourier algebras, we provide the first examples of locally compact groups whose Fourier algebras support non-zero, alternating 2-cocycles; this is the first step in a larger project. Although such 2-cocycles can never be completely bounded, the operator space structure on the Fourier algebra plays a crucial role in our construction, as does the opposite operator space structure.Our construction has two main technical ingredients: we observe that certain estimates from [H. H. Lee, J. Ludwig, E. Samei, N. Spronk, Weak amenability of Fourier algebras and local synthesis of the anti-diagonal, Adv. Math., 292 (2016)] yield derivations that are "co-completely bounded" as maps from various Fourier algebras to their duals; and we establish a twisted inclusion result for certain operator space tensor products, which may be of independent interest.

KW - Alternating cocycle

KW - Co-completely bounded

KW - Fourier algebra

KW - Hochschild cohomology

KW - Opposite operator space

KW - Tensor product

U2 - 10.1016/j.aim.2021.107747

DO - 10.1016/j.aim.2021.107747

M3 - Journal article

VL - 385