{
  "id": "1502.05214",
  "version": "v1",
  "published": "2015-02-18T13:17:53.000Z",
  "updated": "2015-02-18T13:17:53.000Z",
  "title": "Weak amenability of Fourier algebras and local synthesis of the anti-diagonal",
  "authors": [
    "Hun Hee Lee",
    "Jean Ludwig",
    "Ebrahim Samei",
    "Nico Spronk"
  ],
  "comment": "24 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We show that for a connected Lie group $G$, its Fourier algebra $A(G)$ is weakly amenable only if $G$ is abelian. Our main new idea is to show that weak amenability of $A(G)$ implies that the anti-diagonal, $\\check{\\Delta}_G=\\{(g,g^{-1}):g\\in G\\}$, is a set of local synthesis for $A(G\\times G)$. We then show that this cannot happen if $G$ is non-abelian. We conclude for a locally compact group $G$, that $A(G)$ can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group $G$, $A(G)$ is weakly amenable if and only if its connected component of the identity $G_e$ is abelian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-18T13:17:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A30",
      "43A45",
      "43A80",
      "22E15",
      "22D35",
      "46H25",
      "46J40"
    ],
    "keywords": [
      "local synthesis",
      "weak amenability",
      "fourier algebra",
      "anti-diagonal",
      "lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150205214L"
    }
  }
}