{
  "id": "1905.05556",
  "version": "v1",
  "published": "2019-05-14T12:37:47.000Z",
  "updated": "2019-05-14T12:37:47.000Z",
  "title": "Left $φ$-biprojectivity of some Banach algebras",
  "authors": [
    "Amir Sahami"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we introduce a homological notion of left $\\phi$-biprojectivity for Banach algebras, where $\\phi$ is a non-zero multiplicative linear functional. We show that for a locally compact group $G$, the Segal algebra $S(G)$ is left $\\phi$-contractible if and only if $G$ is compact. Also, we prove that the Fourier algebra $A(G)$ is left $\\phi$-biprojective if and only if $G$ is discrete. Finally, we study left $\\phi$-biprojectivity of certain semigroup algebras. We give some examples which show the differences between our new notion and the classical ones.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-14T12:37:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46M10",
      "43A20"
    ],
    "keywords": [
      "banach algebras",
      "biprojectivity",
      "non-zero multiplicative linear functional",
      "fourier algebra",
      "locally compact group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}