{
  "abstract": "We define intrinsic right \\(q\\)-radial vector derivatives on radial algebras of abstract vector variables. For a finite parameter set \\(Y\\), a scalar Jackson calculus on \\(x^2\\) and the mixed anticommutators \\(\\{x,y_i\\}\\) is combined with the exterior decomposition relative to \\(x\\). Relabelling covariance and compatibility under inclusions of parameter sets give a direct-limit operator on arbitrary radial algebras. {Under the dimension specialization \\(Q=q^M\\), its classical limit agrees in every \\(M\\)-dimensional Clifford realization with the standard right Clifford derivative; for an exterior blade one obtains \\([x\\wedge y_I]\\partial_x=(-1)^{|I|}(M-|I|)y_I\\).} Two Fischer-type constructions are considered. The anticommutator with exterior creation is triangular and admits an explicit Green inverse after localization at its diagonal factors. {For right \\(q\\)-monogenic elements, the derivative is paired with right multiplication \\(R_xF=Fx\\). The homogeneous operators \\(\\partial^{Y,\\mathrm R}_{x,q}R_x\\) have generically nonzero determinants, which yields determinant-localized Fischer decompositions and explicit projectors.} The one- and two-vector determinants are computed explicitly. {After \\(Q=q^M\\), the two-vector determinant is nonzero for every \\(0<q<1\\) and every positive integer \\(M\\). For arbitrary finite support, a support filtration factors the determinant into exact-support terms; in degree zero, support rank \\(p\\) contributes the factor \\([m-p]_q+p\\).}",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.00775",
  "author_total": 4,
  "authors": [
    {
      "name": "Diana Barseghyan"
    },
    {
      "name": "Juan Bory-Reyes"
    },
    {
      "name": "Baruch Schneider"
    },
    {
      "name": "Yifan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fw4rxfxb96tph.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.00775",
  "fulltext_url": null,
  "id": "fw4rxfxb96tph",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.00775",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7160013216",
  "pdf_url": "https://arxiv.org/pdf/2605.00775",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fw4rxfxb96tph.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2605.00775",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.00775"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Intrinsic {Right} $q$-Radial Vector Derivatives and Localized Fischer Decompositions on Radial Algebras",
  "title_text": "Intrinsic {Right} q-Radial Vector Derivatives and Localized Fischer Decompositions on Radial Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/fw4rxfxb96tph",
  "venue": "arXiv",
  "versions": []
}