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 Our results complement earlier work of Johnson (JLMS, 1994), Plymen (unpublished note) and Forrest–Samei–Spronk (IUMJ, 2009).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
Uncontrolled Keywords: Coefficient functions ; Cyclic amenability ; Derivations ; Fourier algebra ; Lie group ; Square-integrable representation ; Weak amenability
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 69233
Deposited By: ep_importer_pure
Deposited On: 25 Apr 2014 08:03
Refereed?: Yes
Published?: Published
Last Modified: 11 Jun 2019 01:13
URI: https://eprints.lancs.ac.uk/id/eprint/69233

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