{
  "id": "math/0606366",
  "version": "v4",
  "published": "2006-06-15T15:18:51.000Z",
  "updated": "2007-05-10T23:43:16.000Z",
  "title": "Biflatness of ${\\ell}^1$-semilattice algebras",
  "authors": [
    "Yemon Choi"
  ],
  "comment": "17 pages, accepted by Semigroup Forum. Some details have been added to clarify the closing remarks on the Clifford semigroup case",
  "journal": "Semigroup Forum 75 (2007), no. 2, 253--271.",
  "doi": "10.1007/s00233-007-0730-x",
  "categories": [
    "math.FA",
    "math.RA"
  ],
  "abstract": "Building on an old result of Duncan and Namioka, we show that the ${\\ell}^1$-convolution algebra of a semilattice $S$ is biflat precisely when $S$ is uniformly locally finite. The proof shows in passing that for such $S$ the convolution algebra is isomorphic to ${\\ell}^1(S)$ with pointwise multiplication. At the end we sketch how these techniques may be extended to prove an analogous characterisation of biflatness for Clifford semigroup algebras.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-05-10T23:43:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46M20",
      "46J40",
      "43A20"
    ],
    "keywords": [
      "semilattice algebras",
      "biflatness",
      "convolution algebra",
      "clifford semigroup algebras",
      "old result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6366C"
    }
  }
}