PreprintarXiv licencearXiv
Transfer of Wakamatsu tilting modules along Frobenius extensions
Abstract
Let ι: R→ A be a Frobenius extension and let T be a Wakamatsu tilting left R-module. We give sufficient conditions for the induced module A⊗R T to remain Wakamatsu tilting and establish an ascent--descent result for split centrally projective Frobenius extensions. We also characterize the tilting case by the vanishing of ExtRi(T,A⊗R T) for all i>0. Moreover, if A⊗R T∈addR(T), then the natural map S=EndR(T)→ B=EndA(A⊗R T) of endomorphism rings is a Frobenius extension and T⊗S B≅ A⊗R T as R-B-bimodules. Applications to Brenner--Butler--Miyashita equivalences and some specific classes of Frobenius extensions are also discussed.
Related
- Self-Orthogonal τ-Tilting Modules and Tilting Modules III: Finitistic Dimension
- Self-Orthogonal τ-Tilting Modules and Tilting Modules II: Annihilator Separation
- Relative Derived Delooping Levels and τ-Tilting Modules
- Support τ-tilting modules over Morita context algebras: A bilateral approximation approach
- Relative Suspension and Higher Delooping for Support τ-Tilting Modules
BibTeX
@misc{ren2026transfer,
title = {{Transfer of Wakamatsu tilting modules along Frobenius extensions}},
author = {Wei Ren and Chunxia Zhang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30090},
eprint = {2608.30090},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30090},
}
RIS
TY - UNPB
TI - Transfer of Wakamatsu tilting modules along Frobenius extensions
AU - Wei Ren
AU - Chunxia Zhang
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.30090
UR - https://arxiv.org/abs/2608.30090
AB - Let ι: R→ A be a Frobenius extension and let T be a Wakamatsu tilting left R-module. We give sufficient conditions for the induced module A⊗_R T to remain Wakamatsu tilting and establish an ascent--descent result for split centrally projective Frobenius extensions. We also characterize the tilting case by the vanishing of Ext_R^i(T,A⊗_R T) for all i>0. Moreover, if A⊗_R T∈add_R(T), then the natural map S=End_R(T)→ B=End_A(A⊗_R T) of endomorphism rings is a Frobenius extension and T⊗_S B≅ A⊗_R T as R-B-bimodules. Applications to Brenner--Butler--Miyashita equivalences and some specific classes of Frobenius extensions are also discussed.
ER -