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
Accepted author manuscript, 331 KB, PDF document
Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Accepted author manuscript
Licence: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
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
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
M1 - 107747
ER -