{
  "id": "2302.01611",
  "version": "v1",
  "published": "2023-02-03T09:21:25.000Z",
  "updated": "2023-02-03T09:21:25.000Z",
  "title": "One-quasihomomorphisms from the integers into symmetric matrices",
  "authors": [
    "Tim Seynnaeve",
    "Nafie Tairi",
    "Alejandro Vargas"
  ],
  "comment": "6 pages, 4 figures, comments welcome",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "A function $f$ from $\\mathbb{Z}$ to the symmetric matrices over an arbitrary field $K$ of characteristic $0$ is a $1$-quasihomomorphism if the matrix $f(x+y) - f(x) - f(y)$ has rank at most $1$ for all $x,y \\in \\mathbb{Z}$. We show that any such $1$-quasihomomorphism has distance at most $2$ from an actual group homomorphism. This gives a positive answer to a special case of a problem posed by Kazhdan and Ziegler.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-03T09:21:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B30"
    ],
    "keywords": [
      "symmetric matrices",
      "one-quasihomomorphisms",
      "actual group homomorphism",
      "arbitrary field",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}