{
  "id": "1802.02795",
  "version": "v1",
  "published": "2018-02-08T10:37:49.000Z",
  "updated": "2018-02-08T10:37:49.000Z",
  "title": "An explicit symmetric DGLA model of a triangle",
  "authors": [
    "Itay Griniasty",
    "Ruth Lawrence"
  ],
  "comment": "17 pages, 5 figures",
  "categories": [
    "math.AT"
  ],
  "abstract": "We give explicit formulae for a differential graded Lie algebra (DGLA) model of the triangle which is symmetric under the geometric symmetries of the cell. This follows the work of Lawrence-Sullivan on the (unique) DGLA model of the interval and of Gadish-Griniasty-Lawrence on an explicit symmetric model of the bi-gon. As in the case of the bi-gon, the essential intermediate step is the construction of a symmetric point. Although in this warped geometry of points given by solutions of the Maurer-Cartan equation and lines given by a gauge transformation by Lie algebra elements of grading zero, the medians of a triangle are not concurrent, various other geometric constructions can be carried out. The construction can similarly be applied to give symmetric model of arbitrary $k$-gons.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-08T10:37:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B55",
      "17B01",
      "55U15"
    ],
    "keywords": [
      "explicit symmetric dgla model",
      "explicit symmetric model",
      "differential graded lie algebra",
      "essential intermediate step",
      "construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}