{
  "id": "1709.03889",
  "version": "v1",
  "published": "2017-09-11T01:03:06.000Z",
  "updated": "2017-09-11T01:03:06.000Z",
  "title": "Bilinear forms on Grothendieck groups of triangulated categories",
  "authors": [
    "Peter Webb"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1301.4701",
  "categories": [
    "math.RT"
  ],
  "abstract": "We extend the theory of bilinear forms on the Green ring of a finite group developed by Benson and Parker to the context of the Grothendieck group of a triangulated category with Auslander-Reiten triangles, taking only relations given by direct sum decompositions. We examine the non-degeneracy of the bilinear form given by dimensions of homomorphisms, and show that the form may be modified to give a Hermitian form for which the standard basis given by indecomposable objects has a dual basis given by Auslander-Reiten triangles. An application is given to the homotopy category of perfect complexes over a symmetric algebra, with a consequence analogous to a result of Erdmann and Kerner.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-11T01:03:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G70",
      "18E30",
      "20C20"
    ],
    "keywords": [
      "bilinear form",
      "grothendieck group",
      "triangulated category",
      "auslander-reiten triangles",
      "direct sum decompositions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}