{
  "id": "1807.05549",
  "version": "v1",
  "published": "2018-07-15T13:44:55.000Z",
  "updated": "2018-07-15T13:44:55.000Z",
  "title": "Symmetric tensor categories in characteristic 2",
  "authors": [
    "Dave Benson",
    "Pavel Etingof"
  ],
  "comment": "23 pages, latex",
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct and study a nested sequence of finite symmetric tensor categories ${\\rm Vec}=\\mathcal{C}_0\\subset \\mathcal{C}_1\\subset\\cdots\\subset \\mathcal{C}_n\\subset\\cdots$ over a field of characteristic $2$ such that $\\mathcal{C}_{2n}$ are incompressible, i.e., do not admit tensor functors into tensor categories of smaller Frobenius--Perron dimension. This generalizes the category $\\mathcal{C}_1$ described by Venkatesh and the category $\\mathcal{C}_2$ defined by Ostrik. The Grothendieck rings of the categories $\\mathcal{C}_{2n}$ and $\\mathcal{C}_{2n+1}$ are both isomorphic to the ring of real cyclotomic integers defined by a primitive $2^{n+2}$-th root of unity, $\\mathcal{O}_n=\\mathbb Z[2\\cos(\\pi/2^{n+1})]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-15T13:44:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characteristic",
      "finite symmetric tensor categories",
      "real cyclotomic integers",
      "admit tensor functors",
      "smaller frobenius-perron dimension"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}