{
  "id": "1608.01934",
  "version": "v1",
  "published": "2016-08-05T16:54:07.000Z",
  "updated": "2016-08-05T16:54:07.000Z",
  "title": "Prospecies of algebras I: Basic properties",
  "authors": [
    "Julian Külshammer"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper, we generalise part of the theory of hereditary algebras to the context of prospecies of algebras. Here, a prospecies is a generalisation of Gabriel's concept of species gluing algebras via projective bimodules along a quiver to obtain a new algebra. This provides a categorical perspective on a recent paper by Gei\\ss, Leclerc, and Schr\\\"oer. In particular, we construct a corresponding preprojective algebra, and establish a theory of a separated prospecies yielding a stable equivalence between certain functorially finite subcategories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-05T16:54:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20"
    ],
    "keywords": [
      "basic properties",
      "prospecies",
      "generalise part",
      "functorially finite subcategories",
      "species gluing algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}