{
  "id": "0711.3669",
  "version": "v3",
  "published": "2007-11-23T04:43:02.000Z",
  "updated": "2008-08-14T23:01:03.000Z",
  "title": "Simplicial cohomology of augmentation ideals in ${\\ell}^1(G)$",
  "authors": [
    "Yemon Choi"
  ],
  "comment": "14pp, uses Paul Taylor's diagrams.sty macros. v3: typos caught and some minor corrections/clarifications of terminology. This is not the final version, which will appear in Proc. Edinburgh Math. Soc",
  "journal": "Proc. Edinburgh Math. Soc. 53 (2010), no. 1, 97--109.",
  "doi": "10.1017/S0013091508000060",
  "categories": [
    "math.FA",
    "math.GR"
  ],
  "abstract": "Let $G$ be a discrete group. We give a decomposition theorem for the Hochschild cohomology of $\\ell^1(G)$ with coefficients in certain $G$-modules. Using this we show that if $G$ is commutative-transitive, the canonical inclusion of bounded cohomology of $G$ into simplicial cohomology of $\\ell^1(G)$ is an isomorphism.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-08-14T23:01:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E40",
      "43A20",
      "20E45"
    ],
    "keywords": [
      "simplicial cohomology",
      "augmentation ideals",
      "hochschild cohomology",
      "discrete group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.3669C"
    }
  }
}