{
  "abstract": "Let $T$ be a finite group and let $kB_T$ denote the shifted Burnside biset functor over a commutative ring $k$. We study the essential algebra $\\widehat{kB_T}(G)$ of $kB_T$ at an arbitrary finite group $G$. We first establish criteria determining when a covering subgroup of $G\\times G\\times T$ factors, with respect to the star product, through a group of order strictly smaller than $|G|$; the first criterion places no hypothesis on $T$. As an application, we describe $\\widehat{kB_T}(G)$ completely whenever no nontrivial quotient of $G$ is isomorphic to a section of $T$, extending the coprime case treated by Romero. When $T$ is abelian and $|T|$ is invertible in $k$, we prove that $\\widehat{kB_T}(G)$ decomposes as a direct sum of matrix algebras over the group algebras of the groups $Out_T(A)$, where $A$ runs over the linkage classes of reduced subgroups of $G\\times T$, and we parametrize the simple modules of $\\widehat{kB_T}(G)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08616",
  "author_total": 2,
  "authors": [
    {
      "name": "Olcay Coşkun"
    },
    {
      "name": "Ruslan Muslumov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dx4e2bgf4y246.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08616",
  "fulltext_url": null,
  "id": "dx4e2bgf4y246",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08616",
  "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",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7211986565",
  "pdf_url": "https://arxiv.org/pdf/2609.08616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dx4e2bgf4y246.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08616"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Essential algebra of the shifted Burnside biset functor with abelian shift",
  "title_text": "Essential algebra of the shifted Burnside biset functor with abelian shift",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/dx4e2bgf4y246",
  "venue": "arXiv",
  "versions": []
}