{
  "id": "1809.07510",
  "version": "v1",
  "published": "2018-09-20T07:47:56.000Z",
  "updated": "2018-09-20T07:47:56.000Z",
  "title": "Dihedral and reflexive modules with $\\infty$-simplicial faces and dihedral and reflexive homology of involutive $A_\\infty$-algebras over unital commutative rings",
  "authors": [
    "S. V. Lapin"
  ],
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "The concepts of a dihedral and a reflexive module with $\\infty$-simplicial faces are introduced. For each involutive $A_\\infty$-algebra, the dihedral and the reflexive tensor modules with $\\infty$-simplicial faces are constructed. On the basis of dihedral and reflexive modules with $\\infty$-simplicial faces that defined by an involutive $A_\\infty$-algebra the constructions of the dihedral and the reflexive homology of involutive $A_\\infty$-algebras over any unital commutative rings are given. The conception of an involutive homotopy unital $A_\\infty$-algebra is introduced. A long exact sequence that connecting the dihedral and the reflexive homology of involutive homotopically unital $A_\\infty$-algebras over any unital commutative rings is constructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-20T07:47:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unital commutative rings",
      "simplicial faces",
      "reflexive homology",
      "reflexive module",
      "long exact sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}