{
  "abstract": "Let $(A,T,B)$ be a splitting tilting triple. We provide a construction of $τ_2$-tilting $B$-modules from $τ$-tilting $A$-modules. On the other hand, if $A$ is hereditary, by considering the mutation of a certain two-term silting complex of $A$ and its image under the derived equivalence $\\mathbf{R}{\\rm Hom}_A(T,-):D^b(A)\\to D^b(B)$, we get a three-term silting complex ${\\bf W}$ of $B$. Under an explicit non-vanishing condition on the cones of morphisms between the two summands, we prove that ${\\rm H}^0\\boldsymbol{W}$ is a basic $2$-tilting $B$-module and that it coincides with the module obtained from the first construction. As an application, we generalize the construction of Peng from tilting modules to $τ$-tilting modules. We also determine the endomorphism algebra of the constructed module as an explicit triangular matrix algebra, which is derived equivalent to $A$ and $B$ whenever the constructed module is $2$-tilting, and give a full semi-orthogonal decomposition of $K^b(\\operatorname{proj}A)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22989",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhongyuan Wang"
    },
    {
      "name": "Haicheng Zhang"
    },
    {
      "name": "Tiwei Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/258767jcv97pf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22989",
  "fulltext_url": null,
  "id": "258767jcv97pf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22989",
  "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.CT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214026577",
  "pdf_url": "https://arxiv.org/pdf/2609.22989",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/258767jcv97pf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22989",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22989"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "From $τ$-tilting to $τ_2$-tilting via splitting tilting triples",
  "title_text": "From τ-tilting to τ_2-tilting via splitting tilting triples",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/258767jcv97pf",
  "venue": "arXiv",
  "versions": []
}