Home > Research > Publications & Outputs > Constructing alternating 2-cocycles on Fourier ...

Electronic data

  • 2008.02226

    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

    Embargo ends: 22/04/22

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

Links

Text available via DOI:

View graph of relations

Constructing alternating 2-cocycles on Fourier algebras

Research output: Contribution to journalJournal articlepeer-review

E-pub ahead of print
Article number107747
<mark>Journal publication date</mark>16/07/2021
<mark>Journal</mark>Advances in Mathematics
Volume385
Number of pages28
Publication StatusE-pub ahead of print
Early online date22/04/21
<mark>Original language</mark>English

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.

Bibliographic note

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