PreprintCC BY 4.0arXiv
Tensor Product Does Not Behave Additively on Delooping Level
Abstract
The Finitistic Dimension Conjecture is one of the most important homological conjectures in the representation theory of finite-dimensional algebras. Recently, Gélinas arXiv:2004.04828 proposed the notion of "delooping level" to study the finitistic dimension Conjecture. This article reports a misconception between the delooping level and the tensor product of algebras. Namely, for finite-dimensional algebras A and B, the difference dell(A⊗kB) − (dell(A)+ dell(B)) can be arbitrarily large or negative.
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BibTeX
@misc{lam2026tensor,
title = {{Tensor Product Does Not Behave Additively on Delooping Level}},
author = {Ryan Lam},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39745},
eprint = {2609.39745},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39745},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tensor Product Does Not Behave Additively on Delooping Level
AU - Ryan Lam
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2609.39745
UR - https://arxiv.org/abs/2609.39745
AB - The Finitistic Dimension Conjecture is one of the most important homological conjectures in the representation theory of finite-dimensional algebras. Recently, Gélinas arXiv:2004.04828 proposed the notion of "delooping level" to study the finitistic dimension Conjecture. This article reports a misconception between the delooping level and the tensor product of algebras. Namely, for finite-dimensional algebras A and B, the difference dell(A⊗_kB) − (dell(A)+ dell(B)) can be arbitrarily large or negative.
ER -