{
  "id": "1705.03367",
  "version": "v1",
  "published": "2017-05-09T14:54:29.000Z",
  "updated": "2017-05-09T14:54:29.000Z",
  "title": "Special tilting modules for algebras with positive dominant dimension",
  "authors": [
    "Matthew Pressland",
    "Julia Sauter"
  ],
  "comment": "29 pages, comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study a set of uniquely determined tilting and cotilting modules for an algebra with positive dominant dimension, with the property that they are generated or cogenerated (and usually both) by projective-injectives. These modules have various interesting properties, for example that their endomorphism algebras always have global dimension at most that of the original algebra. We characterise d-Auslander-Gorenstein algebras and d-Auslander algebras via the property that the relevant tilting and cotilting modules coincide. By the Morita-Tachikawa correspondence, any algebra of dominant dimension at least 2 may be expressed (essentially uniquely) as the endomorphism algebra of a generator-cogenerator for another algebra, and we also study our special tilting and cotilting modules from this point of view, via the theory of recollements and intermediate extension functors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-09T14:54:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "18E30",
      "18G05"
    ],
    "keywords": [
      "positive dominant dimension",
      "special tilting modules",
      "endomorphism algebra",
      "characterise d-auslander-gorenstein algebras",
      "intermediate extension functors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}