{
  "id": "2102.11940",
  "version": "v1",
  "published": "2021-02-23T21:04:07.000Z",
  "updated": "2021-02-23T21:04:07.000Z",
  "title": "Geometric invariant decomposition of SU(3)",
  "authors": [
    "Martin Roelfs"
  ],
  "comment": "7 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A novel invariant decomposition of diagonalizable $n \\times n$ matrices into $n$ commuting matrices is presented. This decomposition is subsequently used to split the fundamental representation of $\\mathfrak{su}(3)$ Lie algebra elements into at most three commuting elements of $\\mathfrak{u}(3)$. As a result, the exponential of an $\\mathfrak{su}(3)$ Lie algebra element can be split into three commuting generalized Euler's formulas, or conversely, a Lie group element can be factorized into at most three generalized Euler's formulas. After the factorization has been performed, the logarithm follows immediately.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-23T21:04:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric invariant decomposition",
      "lie algebra element",
      "generalized eulers formulas",
      "lie group element",
      "novel invariant decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}