Constructing alternating 2-cocycles on Fourier algebras

Choi, Yemon (2021) Constructing alternating 2-cocycles on Fourier algebras. Advances in Mathematics, 385: 107747. ISSN 0001-8708

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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.

Item Type:
Journal Article
Journal or Publication Title:
Advances in Mathematics
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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
Uncontrolled Keywords:
?? alternating cocycleco-completely boundedfourier algebrahochschild cohomologyopposite operator spacetensor productmathematics(all) ??
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Deposited On:
30 Mar 2021 08:50
Last Modified:
21 Apr 2024 00:46