{
  "id": "math/0609450",
  "version": "v4",
  "published": "2006-09-15T16:15:08.000Z",
  "updated": "2008-02-25T09:14:58.000Z",
  "title": "Simplicial homology of strong semilattices of Banach algebras",
  "authors": [
    "Yemon Choi"
  ],
  "comment": "28 pages, final arXiv version. Slight improvement to abstract and MSC; minor changes to LaTeX (spacing, line breaks, use of double subscripts, etc.); correction of a few more typos. A leaner version of this paper will appear in the Houston Journal of Mathematics",
  "journal": "Houston J. Math. 36 (2010), no. 1, 237--260.",
  "categories": [
    "math.FA",
    "math.CT",
    "math.RA"
  ],
  "abstract": "Certain semigroups are known to admit a `strong semilattice decomposition' into simpler pieces. We introduce a class of Banach algebras that generalise the $\\ell^1$-convolution algebras of such semigroups, and obtain a disintegration theorem for their simplicial homology. Using this we show that for any Clifford semigroup $S$ of amenable groups, $\\lp{1}(S)$ is simplicially trivial: this generalises results in \\cite{YC_GMJ}. Some other applications are presented.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2008-02-25T09:14:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46M20",
      "16E40",
      "43A20"
    ],
    "keywords": [
      "banach algebras",
      "simplicial homology",
      "strong semilattice decomposition",
      "generalises results",
      "convolution algebras"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9450C"
    }
  }
}