{
  "id": "1505.04980",
  "version": "v1",
  "published": "2015-05-19T13:01:31.000Z",
  "updated": "2015-05-19T13:01:31.000Z",
  "title": "Tensor products of higher almost split sequences",
  "authors": [
    "Andrea Pasquali"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama gave a precise criterion for when the tensor product of an $n$-representation finite algebra and an $m$-representation finite algebra is $(n+m)$-representation finite. In this case we give a complete description of the higher almost split sequences over the tensor product by expressing every higher almost split sequence as the mapping cone of a suitable chain map and using a natural notion of tensor product for chain maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-19T13:01:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16G70"
    ],
    "keywords": [
      "tensor product",
      "split sequence",
      "representation finite algebra",
      "precise criterion",
      "iyama gave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}