{
  "id": "math/0307060",
  "version": "v1",
  "published": "2003-07-04T10:34:14.000Z",
  "updated": "2003-07-04T10:34:14.000Z",
  "title": "Derived Categories of Nodal Algebras",
  "authors": [
    "Igor Burban",
    "Yuriy Drozd"
  ],
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "In this article we classify indecomposable objects of the derived categories of finitely-generated modules over certain infinite-dimensional algebras. The considered class of algebras (which we call nodal algebras) contains such well-known algebras as the complete ring of a double nodal point $\\kk[[x,y]]/(xy)$ and the completed path algebra of the Gelfand quiver. As a corollary we obtain a description of the derived category of Harish-Chandra modules over $SL_{2}({\\mathbb R})$. We also give an algorithm, which allows to construct projective resolutions of indecomposable complexes. In the appendix we prove the Krull-Schmidt theorem for homotopy categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-07-04T10:34:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16G60"
    ],
    "keywords": [
      "derived category",
      "nodal algebras",
      "homotopy categories",
      "krull-schmidt theorem",
      "gelfand quiver"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7060B"
    }
  }
}