{
  "abstract": "We study quiver Demazure algebras through residue covers and root-power quotients. The cover determined by the zero-root subsystem identifies the additive algebra with a finite fixed algebra of Sauter's generalized quiver Hecke construction. Her basis theorem then gives additive PBW in every finite Weyl type, for arbitrary admissible residue data and uniform quivers. A sequence-cover argument gives global multiplicative PBW in simply-laced type. Under a directed-path condition, root-power quotients are finite dimensional and the formal exponential identifies their additive and multiplicative forms. For arrow-free quivers, we reduce mixed-residue quotients to matrix algebras over finite skew group rings, obtain sharp nonvanishing criteria from coinvariant geometry, and determine their simple modules. In a mixed type-$D_4$ family we compute an explicit coefficient presentation, dimensions, Loewy lengths, and Cartan matrices. We also specify the direct and finite-cover comparisons with Liu's algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08431",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhi-Wei Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/azd439naw96a4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08431",
  "fulltext_url": null,
  "id": "azd439naw96a4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08431",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221041091",
  "pdf_url": "https://arxiv.org/pdf/2610.08431",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/azd439naw96a4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08431",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08431"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quiver Demazure algebras I: Residue descent, finite quotients, and PBW bases",
  "title_text": "Quiver Demazure algebras I: Residue descent, finite quotients, and PBW bases",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/azd439naw96a4",
  "venue": "arXiv",
  "versions": []
}