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Derived Delooping Levels of One-Point Extensions and Finitistic Dimensions
Abstract
Let B be a finite-dimensional algebra, M∈modu B, and A=B[M] the one-point extension. We give a stable two-step extension criterion for the new simple A-module to have derived delooping level at most one. For a concrete algebra B with a self-injective Nakayama quotient R, we determine the derived and classical delooping levels of B[M] for every nonzero M∈modu R. In particular, we obtain an explicit algebra A satisfying Findim(Aop)=1<2=ddell A=dell A, which gives a negative answer to a question of Guo and Igusa.
Related
BibTeX
@misc{gao2026derived,
title = {{Derived Delooping Levels of One-Point Extensions and Finitistic Dimensions}},
author = {Hanpeng Gao and Dajun Liu and Ruomu Xu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32744},
eprint = {2609.32744},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32744},
}
RIS
TY - UNPB
TI - Derived Delooping Levels of One-Point Extensions and Finitistic Dimensions
AU - Hanpeng Gao
AU - Dajun Liu
AU - Ruomu Xu
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32744
UR - https://arxiv.org/abs/2609.32744
AB - Let B be a finite-dimensional algebra, M∈modu B, and A=B[M] the one-point extension. We give a stable two-step extension criterion for the new simple A-module to have derived delooping level at most one. For a concrete algebra B with a self-injective Nakayama quotient R, we determine the derived and classical delooping levels of B[M] for every nonzero M∈modu R. In particular, we obtain an explicit algebra A satisfying Findim(A^op)=1<2=ddell A=dell A, which gives a negative answer to a question of Guo and Igusa.
ER -