{
  "abstract": "We consider a family $(Λ_λ)_{λ\\in \\Bbbk^\\times}$ of weakly symmetric algebras of Euclidean type over an algebraically closed field $\\Bbbk$, where $\\Bbbk^\\times:= \\Bbbk\\setminus \\{0\\}$, and for each $λ\\in \\Bbbk^\\times$, $Λ_λ$ is socle equivalent to $Λ_1$, which is the trivial extension of a hereditary algebra of type $\\tilde{A}$. We compute their Hochschild cohomologies, which shows that $Λ_λ$ is not derived equivalent to $Λ_1$ if $λ\\neq 1$. This means that a derived equivalence classification of weakly symmetric algebras of Euclidean type given by Bocian--Holm--Skowro{\\' n}ski is not complete.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15517",
  "author_total": 3,
  "authors": [
    {
      "name": "Hideto Asashiba"
    },
    {
      "name": "Ayako Itaba"
    },
    {
      "name": "Manuel Saorin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4kh8ecw2pacnf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15517",
  "fulltext_url": null,
  "id": "4kh8ecw2pacnf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15517",
  "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.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221824535",
  "pdf_url": "https://arxiv.org/pdf/2610.15517",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4kh8ecw2pacnf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15517",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15517"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On a derived equivalence classification of weakly symmetric algebras of Euclidean type",
  "title_text": "On a derived equivalence classification of weakly symmetric algebras of Euclidean type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/4kh8ecw2pacnf",
  "venue": "arXiv",
  "versions": []
}