Weak and cyclic amenability for Fourier algebras of connected Lie groups

Choi, Yemon and Ghandehari, Mahya (2014) Weak and cyclic amenability for Fourier algebras of connected Lie groups. Journal of Functional Analysis, 266 (11). pp. 6501-6530. ISSN 0022-1236

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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 Our results complement earlier work of Johnson (JLMS, 1994), Plymen (unpublished note) and Forrest–Samei–Spronk (IUMJ, 2009).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.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Functional Analysis
Additional Information:
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
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2603
Subjects:
ID Code:
155325
Deposited By:
Deposited On:
25 May 2021 08:55
Refereed?:
Yes
Published?:
Published
Last Modified:
07 Dec 2021 02:23