Support τ-tilting modules over Morita context algebras: A bilateral approximation approach

@misc{zhang2026support,
  title = {{Support $τ$-tilting modules over Morita context algebras: A bilateral approximation approach}},
  author = {Yingying Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18746},
  eprint = {2609.18746},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18746},
}

TY  - UNPB
TI  - Support τ-tilting modules over Morita context algebras: A bilateral approximation approach
AU  - Yingying Zhang
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18746
UR  - https://arxiv.org/abs/2609.18746
AB  - Let k be a field and let Λ=(A&N M&B)_ϕ,ψ be a finite-dimensional Morita context algebra. We introduce a bilateral approximation construction which glues support τ-tilting modules over A and B by alternately correcting the two corner components through minimal approximations and pushouts. When this process terminates, it yields a support τ-tilting Λ-module with the prescribed componentwise torsion class. The one-sided case recovers Zhang's triangular-matrix construction, while the two-sided compatibility conditions give direct corner induction and, for radical-valued connecting maps, are also necessary, extending the Gao--Huang criterion. Examples show that the bilateral correction process can terminate even when neither one-sided compatibility condition is satisfied, while in other examples the process never terminates.
ER  -