{
  "id": "2210.17231",
  "version": "v1",
  "published": "2022-10-31T11:19:23.000Z",
  "updated": "2022-10-31T11:19:23.000Z",
  "title": "Separated monic correspondence of cotorsion pairs and semi-Gorenstein-projective modules",
  "authors": [
    "Xiu-Hua Luo",
    "Shijie Zhu"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Given a finite dimensional algebra $A$ over a field $k$, and a finite acyclic quiver $Q$, let $\\Lambda = A\\otimes_k kQ/I$, where $kQ$ is the path algebra of $Q$ over $k$ and $I$ is a monomial ideal. We show that $(\\mathcal X,\\mathcal Y)$ is a (complete) hereditary cotorsion pair in $A$-mod if and only if $({\\rm smon}(Q,I,\\mathcal X), {\\rm rep}(Q,I,\\mathcal Y))$ is a (complete) hereditary cotorsion pair in $\\Lambda$-mod. We also show that $A$ is left weakly Gorenstein if and only if so is $\\Lambda$. Provided that $kQ/I$ is non-semisimple, the category $^{\\perp}\\Lambda$ of semi-Gorenstein-projective $\\Lambda$-modules coincides with the category of separated monic representations ${\\rm smon}(Q,I,^{\\perp}A)$ if and only if $A$ is left weakly Gorenstein.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-31T11:19:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16G50",
      "16E65",
      "16B50"
    ],
    "keywords": [
      "separated monic correspondence",
      "semi-gorenstein-projective modules",
      "hereditary cotorsion pair",
      "left weakly gorenstein",
      "finite acyclic quiver"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}