{
  "id": "1004.2301",
  "version": "v2",
  "published": "2010-04-14T01:27:52.000Z",
  "updated": "2011-06-28T00:22:12.000Z",
  "title": "Simplicial cohomology of band semigroup algebras",
  "authors": [
    "Yemon Choi",
    "Frédéric Gourdeau",
    "Michael C. White"
  ],
  "comment": "v1: AMS-LaTeX, 24 pages, 1 figure. v2: some typos corrected; a few minor adjustments made for clarity; references updated. Accepted June 2011 by Proc. Royal Soc. Edinburgh Sect. A",
  "journal": "Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 4, 715--744",
  "doi": "10.1017/S0308210510000648",
  "categories": [
    "math.FA"
  ],
  "abstract": "We establish simplicial triviality of the convolution algebra $\\ell^1(S)$, where $S$ is a band semigroup. This generalizes results of the first author [Glasgow Math. J. 2005, Houston J. Math. 2010]. To do so, we show that the cyclic cohomology of this algebra vanishes in all odd degrees, and is isomorphic in even degrees to the space of continuous traces on $\\ell^1(S)$. Crucial to our approach is the use of the structure semilattice of $S$, and the associated grading of $S$, together with an inductive normalization procedure in cyclic cohomology; the latter technique appears to be new, and its underlying strategy may be applicable to other convolution algebras of interest.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-28T00:22:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E40",
      "43A20"
    ],
    "keywords": [
      "band semigroup algebras",
      "simplicial cohomology",
      "cyclic cohomology",
      "convolution algebra",
      "establish simplicial triviality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.2301C"
    }
  }
}