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From τ-tilting to τ2-tilting via splitting tilting triples

  • Zhongyuan Wang
  • Haicheng Zhang
  • Tiwei Zhao
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Abstract

Let (A,T,B) be a splitting tilting triple. We provide a construction of τ2-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 RHomA(T,−):Db(A)→ Db(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 H0W 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 Kb(projA).

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Cite

BibTeXRIS
BibTeX
@misc{wang2026from,
  title = {{From $τ$-tilting to $τ_2$-tilting via splitting tilting triples}},
  author = {Zhongyuan Wang and Haicheng Zhang and Tiwei Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22989},
  eprint = {2609.22989},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22989},
}
RIS
TY  - UNPB
TI  - From τ-tilting to τ_2-tilting via splitting tilting triples
AU  - Zhongyuan Wang
AU  - Haicheng Zhang
AU  - Tiwei Zhao
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22989
UR  - https://arxiv.org/abs/2609.22989
AB  - 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 RHom_A(T,−):D^b(A)→ 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 H^0W 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(projA).
ER  -