{
  "id": "2301.13205",
  "version": "v1",
  "published": "2023-01-29T14:14:16.000Z",
  "updated": "2023-01-29T14:14:16.000Z",
  "title": "Representations and identities of Baxter monoids with involution",
  "authors": [
    "Bin Bin Han",
    "Wen Ting Zhang",
    "Yan Feng Luo",
    "Jin Xing Zhao"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2301.12449",
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "Let $(\\mathsf{baxt}_n,~^\\sharp)$ be the Baxter monoid of finite rank $n$ with Sch\\\"{u}tzenberger's involution $^{\\sharp}$. In this paper, it is shown that $(\\mathsf{baxt}_n,~^\\sharp)$ admits a faithful representation by an involution monoid of upper triangular matrices over any semiring from a large class including the tropical semiring under the skew transposition. Then a transparent combinatorial characterization of the word identities satisfied by $(\\mathsf{baxt}_n,~^\\sharp)$ is given. Further, it is proved that $(\\mathsf{baxt}_n,~^\\sharp)$ is finitely based if and only if $n\\neq 3$, and shown that the identity checking problem for $(\\mathsf{baxt}_n,~^\\sharp)$ can be done in polynomial time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-29T14:14:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M07",
      "20M30",
      "05E99",
      "12K10",
      "16Y60"
    ],
    "keywords": [
      "baxter monoid",
      "representation",
      "transparent combinatorial characterization",
      "upper triangular matrices",
      "word identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}