{
  "abstract": "We classify all abstract automorphisms of the elementary and full twisted Chevalley groups of types ${}^2A_\\ell$ ($\\ell\\geq3$), ${}^2D_\\ell$ ($\\ell\\geq4$), ${}^2E_6$, and ${}^3D_4$ over arbitrary commutative rings, for every invariant isogeny type. The coefficient automorphism $θ$ has order dividing that of the diagram automorphism. We assume that $2$ is invertible and, for triality, that $3$ is invertible as well. Three features distinguish the answer from the usual inner--diagonal and coefficient decomposition. The elementary groups of types ${}^2A_3$ and ${}^2A_4$ admit an additive family of exceptional automorphisms supported at $θ$-fixed maximal ideals with residue field $\\mathbb F_3$. In type ${}^2D_4$, diagram automorphisms may vary on idempotent components, subject to compatibility with the involution and the isogeny lattice. In triality, the coefficient automorphisms preserve the trace operator $r\\mapsto r+θ(r)+θ^2(r)$ but need not commute with $θ$. We determine which elementary automorphisms extend to the full groups and describe the remaining central factors. A nonzero exceptional unitary factor extends precisely in the simply connected type ${}^2A_3$, giving a classification for the hyperbolic group $\\operatorname{SU}_4(R,θ;Q_4)$. The proof glues uniquely determined normalization data for a finite root frame and then recovers the coefficient action from root-subgroup relations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30314",
  "author_total": 2,
  "authors": [
    {
      "name": "Elena I. Bunina"
    },
    {
      "name": "Deep H. Makadiya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4vrbhbstyb83.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30314",
  "fulltext_url": null,
  "id": "d4vrbhbstyb83",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30314",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223376111",
  "pdf_url": "https://arxiv.org/pdf/2610.30314",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4vrbhbstyb83.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30314",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30314"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Automorphisms of Twisted Chevalley Groups over Commutative Rings",
  "title_text": "Automorphisms of Twisted Chevalley Groups over Commutative Rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/d4vrbhbstyb83",
  "venue": "arXiv",
  "versions": []
}