{
  "id": "1209.5096",
  "version": "v2",
  "published": "2012-09-23T18:40:24.000Z",
  "updated": "2015-01-20T03:09:11.000Z",
  "title": "Path methods for strong shift equivalence of positive matrices",
  "authors": [
    "Mike Boyle",
    "K. H. Kim",
    "F. W. Roush"
  ],
  "comment": "This version adds a 3-part program for studying SEE over the reals. One part is handled by the arxiv post \"Strong shift equivalence and algebraic K-theory\". This version is the author version of the paper published in the Kim memorial volume. From that, my short lifestory of Kim (and more) is on my web page http://www.math.umd.edu/~mboyle/papers/index.html",
  "journal": "Acta Appl. Math. 126 (2013) 66-115",
  "doi": "10.1007/S10440-013-9809-4",
  "categories": [
    "math.DS"
  ],
  "abstract": "In the early 1990's, Kim and Roush developed path methods for establishing strong shift equivalence (SSE) of positive matrices over a dense subring U of the real numbers R. This paper gives a detailed, unified and generalized presentation of these path methods. New arguments which address arbitrary dense subrings U of R are used to show that for any dense subring U of R, positive matrices over U which have just one nonzero eigenvalue and which are strong shift equivalent over U must be strong shift equivalent over U_+. In addition, we show positive real matrices on a path of shift equivalent positive real matrices are SSE over R_+; positive rational matrices which are SSE over R_+ must be SSE over Q_+; and for any dense subring U of R, within the set of positive matrices over U which are conjugate over U to a given matrix, there are only finitely many SSE-U_+ classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-23T18:40:24.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-20T03:09:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10"
    ],
    "keywords": [
      "strong shift equivalence",
      "positive matrices",
      "path methods",
      "strong shift equivalent",
      "shift equivalent positive real matrices"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.5096B"
    }
  }
}