PreprintCC BY 4.0arXiv
Reduction techniques for the derived delooping levels
Abstract
The derived delooping level is a recently introduced homological invariant that provides an upper bound for the finitistic dimension of the opposite algebra. In this paper, we employ two reduction techniques-cleft extensions and recollements-to study the finiteness of the derived delooping level of finite-dimensional algebras over a field. By applying the theory of cleft extensions to bound quiver algebras, we establish arrow-removal operations that preserve the finiteness of the derived delooping level. In parallel, using recollement techniques, we develop vertex-removal operations with the same finiteness-preserving property. We conclude with several examples illustrating the applicability and effectiveness of these reduction methods.
Related
- Derived Delooping Levels of One-Point Extensions and Finitistic Dimensions
- Relative Derived Delooping Levels and τ-Tilting Modules
- Relative derived delooping levels and torsion intervals
- Degree-shifted derived invariance of derived delooping levels
- Counterexamples and gap phenomena for derived delooping levels
BibTeX
@misc{wu2026reduction,
title = {{Reduction techniques for the derived delooping levels}},
author = {Kaili Wu and Jiaqun Wei and Dajun Liu and Weiqing Cao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16957},
eprint = {2609.16957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16957},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reduction techniques for the derived delooping levels
AU - Kaili Wu
AU - Jiaqun Wei
AU - Dajun Liu
AU - Weiqing Cao
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16957
UR - https://arxiv.org/abs/2609.16957
AB - The derived delooping level is a recently introduced homological invariant that provides an upper bound for the finitistic dimension of the opposite algebra. In this paper, we employ two reduction techniques-cleft extensions and recollements-to study the finiteness of the derived delooping level of finite-dimensional algebras over a field. By applying the theory of cleft extensions to bound quiver algebras, we establish arrow-removal operations that preserve the finiteness of the derived delooping level. In parallel, using recollement techniques, we develop vertex-removal operations with the same finiteness-preserving property. We conclude with several examples illustrating the applicability and effectiveness of these reduction methods.
ER -