{
  "id": "1401.2558",
  "version": "v1",
  "published": "2014-01-11T19:40:30.000Z",
  "updated": "2014-01-11T19:40:30.000Z",
  "title": "Phi-Homological Properties of Beurling Algebras",
  "authors": [
    "A. Sahami",
    "A. Pourabbas"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we investigate ?-homological properties for Beurling algebras, where ? is a character on those Banach algebras. We show that L1(G;w) is ?0-biprojective if and only if G is compact, where ?0 is the augmentation character. Also we show that M(G;w) is ?i0 0 -biprojective if and only if G is a compact group, where ?i0 0 is an extension of augmentation character to M(G;w). We de?ne the notion of character-projective Banach A-bimodules and also ?-split and ?-admissible triples. We show that L1(G) is amenable if and only if some particular ?-admissible triples of Banach L1(G)-bimodules are ?-split triples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-11T19:40:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A07",
      "43A20",
      "46H05"
    ],
    "keywords": [
      "beurling algebras",
      "phi-homological properties",
      "augmentation character",
      "banach algebras",
      "compact group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.2558S"
    }
  }
}