{
  "id": "1304.5289",
  "version": "v1",
  "published": "2013-04-19T00:52:13.000Z",
  "updated": "2013-04-19T00:52:13.000Z",
  "title": "Split-by-nilpotent extensions algebras and stratifying systems",
  "authors": [
    "Marcelo Lanzilotta",
    "Octavio Mendoza",
    "Corina Sáenz"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\Gamma$ and $\\Lambda$ be artin algebras such that $\\Gamma$ is a split-by-nilpotent extension of $\\Lambda$ by a two sided ideal $I$ of $\\Gamma.$ Consider the so-called change of rings functors $G:={}_\\Gamma\\Gamma_\\Lambda\\otimes_\\Lambda -$ and $F:={}_\\Lambda \\Lambda_\\Gamma\\otimes_\\Gamma -.$ In this paper, we find the necessary and sufficient conditions under which a stratifying system $(\\Theta,\\leq)$ in $\\modu\\Lambda$ can be lifted to a stratifying system $(G\\Theta,\\leq)$ in $\\modu\\,(\\Gamma).$ Furthermore, by using the functors $F$ and $G,$ we study the relationship between their filtered categories of modules and some connections with their corresponding standardly stratified algebras are stated. Finally, a sufficient condition is given for stratifying systems in $\\modu\\,(\\Gamma)$ in such a way that they can be restricted, through the functor $F,$ to stratifying systems in $\\modu\\,(\\Lambda).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-19T00:52:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "18G99"
    ],
    "keywords": [
      "stratifying system",
      "split-by-nilpotent extensions algebras",
      "sufficient condition",
      "rings functors",
      "artin algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.5289L"
    }
  }
}