{
  "id": "0811.4336",
  "version": "v6",
  "published": "2008-11-26T15:11:46.000Z",
  "updated": "2013-10-05T00:51:11.000Z",
  "title": "Invariants of stationary AF-algebras and torsion subgroup of elliptic curves with complex multiplication",
  "authors": [
    "Igor Nikolaev"
  ],
  "comment": "12 pages, to appear Missouri J. Math. Sci",
  "journal": "Missouri J. Math. Sci. 26 (2014), 23-32",
  "categories": [
    "math.NT",
    "math.OA"
  ],
  "abstract": "Let G(A) be an AF-algebra given by periodic Bratteli diagram with the incidence matrix A in GL(n, Z). For a given polynomial p(x) in Z[x] we assign to G(A) a finite abelian group Z^n/p(A) Z^n. It is shown that if p(0)=1 or p(0)=-1 and Z[x]/(p(x)) is a principal ideal domain, then Z^n/p(A) Z^n is an invariant of the strong stable isomorphism class of G(A). For n=2 and p(x)=x-1 we conjecture a formula linking values of the invariant and torsion subgroup of elliptic curves with complex multiplication.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2013-10-05T00:51:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G15",
      "46L85"
    ],
    "keywords": [
      "complex multiplication",
      "elliptic curves",
      "torsion subgroup",
      "stationary af-algebras",
      "strong stable isomorphism class"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.4336N"
    }
  }
}