{
  "abstract": "Let $R$ be a field and $A$ the endomorphism algebra of a finite direct sum of cyclic modules over a finite-dimensional commutative local principal ideal $R$-algebra. We construct a central quotient showing that the support $τ$-tilting poset of $A$ is isomorphic to the poset of the symmetric group with the weak order. We show that the center of $A$ and degree-zero Hochschild homology, viewed as a module over the center, determine the truncated local algebra and the multiset of successive length gaps. For centralizer matrix algebras, the support $τ$-tilting poset determines the multiset of distinct-exponent counts of the primary blocks. The corresponding algebra--module pair also recovers their local algebras and gap multisets. Combining this reconstruction with the known derived equivalence classification, we characterize derived equivalence by isomorphism of these algebra-module pairs. We apply the results to Morita reconstruction in the string and gentle classes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.15460",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiangsheng Hu"
    },
    {
      "name": "Yu-Zhe Liu"
    },
    {
      "name": "Tiwei Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ekfgrdm0haf5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.15460",
  "fulltext_url": null,
  "id": "3ekfgrdm0haf5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.15460",
  "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.RA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7203680928",
  "pdf_url": "https://arxiv.org/pdf/2608.15460",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ekfgrdm0haf5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2608.15460",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.15460"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Support $τ$-tilting posets and Hochschild reconstruction for matrix centralizer algebras",
  "title_text": "Support τ-tilting posets and Hochschild reconstruction for matrix centralizer algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/3ekfgrdm0haf5",
  "venue": "arXiv",
  "versions": []
}