{
  "abstract": "We study the algebraic structure of $(6,3)$ biangular Parseval frames. The two-distance property yields adjacency matrices $A_1,A_2$ whose span forms a three-dimensional commutative algebra, and adjoining the commutator $[A_1,A_2]$ produces a three-dimensional Lie algebra $\\g$. The Gram matrix $G = I + c_1 A_1 + c_2 A_2$ induces a derivation $α(X) = [G,X]$ on $\\g$, equipping $(\\g, [\\cdot,\\cdot], α)$ with a Hom--Lie algebra structure. We compute all structure constants explicitly in terms of the strongly regular graph parameters $(k_1,λ_1,μ_1,k_2,λ_2,μ_2)$ and the frame angles $(c_1,c_2)$, and use this framework to derive explicit bounds for the partial frame operators arising in Marcus--Spielman--Srivastava (MSS) partitions. These bounds depend directly on the structure constants and refine the universal MSS estimate in the regime of highly unbalanced partitions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00215",
  "author_total": 3,
  "authors": [
    {
      "name": "Abraham Orinda"
    },
    {
      "name": "Geoffrey Mboya"
    },
    {
      "name": "Arvince Ogendi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ckdg4xaz8867.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00215",
  "fulltext_url": null,
  "id": "9ckdg4xaz8867",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00215",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7206210011",
  "pdf_url": "https://arxiv.org/pdf/2609.00215",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ckdg4xaz8867.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00215",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00215"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Hom--Lie Algebras and Explicit MSS Partition Bounds for $(6,3)$ Biangular Frames",
  "title_text": "Hom--Lie Algebras and Explicit MSS Partition Bounds for (6,3) Biangular Frames",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/9ckdg4xaz8867",
  "venue": "arXiv",
  "versions": []
}