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  • 1304.3710v4

    Rights statement: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. 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 in Journal of Functional Analysis, [266, 11, (2014)] DOI: 10.1016/j.jfa.2014.03.012

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Weak and cyclic amenability for Fourier algebras of connected Lie groups

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<mark>Journal publication date</mark>1/06/2014
<mark>Journal</mark>Journal of Functional Analysis
Issue number11
Volume266
Number of pages30
Pages (from-to)6501-6530
Publication StatusPublished
Early online date13/04/14
<mark>Original language</mark>English

Abstract

Using techniques of non-abelian harmonic analysis, we construct an explicit, non-zero cyclic derivation on the Fourier algebra of the real ax+b group. In particular this provides the first proof that this algebra is not weakly amenable. Using the structure theory of Lie groups, we deduce that the Fourier algebras of connected, semisimple Lie groups also support non-zero, cyclic derivations and are likewise not weakly amenable. Our results complement earlier work of Johnson (JLMS, 1994), Plymen (unpublished note) and Forrest–Samei–Spronk (IUMJ, 2009). As an additional illustration of our techniques, we construct an explicit, non-zero cyclic derivation on the Fourier algebra of the reduced Heisenberg group, providing the first example of a connected nilpotent group whose Fourier algebra is not weakly amenable.

Bibliographic note

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. 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 in Journal of Functional Analysis, [266, 11, (2014)] DOI: 10.1016/j.jfa.2014.03.012