{
  "id": "2307.10715",
  "version": "v1",
  "published": "2023-07-20T09:17:42.000Z",
  "updated": "2023-07-20T09:17:42.000Z",
  "title": "The Auslander-Reiten theory of the morphism category of projective modules",
  "authors": [
    "Rasool Hafezi",
    "Jiaqun Wei"
  ],
  "comment": "Any comments are welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "We investigate the structure of certain almost split sequences in $\\mathcal{P}(\\Lambda)$, i.e., the category of morphisms between projective modules over an Artin algebra $\\Lambda$. The category $\\mathcal{P}(\\Lambda)$ has very nice properties and is closely related to $\\tau$-tilting theory, $g$-vectors, and Auslander-Reiten theory. We provide explicit constructions of certain almost split sequences ending at or starting from certain objects. Applications, such as to $g$-vectors, are given. As a byproduct, we also show that there exists an injection from Morita equivalence classes of Artin algebras to equivalence classes of 0-Auslander exact categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-20T09:17:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "auslander-reiten theory",
      "projective modules",
      "morphism category",
      "split sequences",
      "artin algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}