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arXiv · 2609.39745

Tensor Product Does Not Behave Additively on Delooping Level

Ryan Lam
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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 $\operatorname{dell}(A\otimes_{\mathbf{k}}B) - \left(\operatorname{dell}(A)+ \operatorname{dell}(B)\right)$ can be arbitrarily large or negative.

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Ryan Lam. 2026-10-07. Tensor Product Does Not Behave Additively on Delooping Level. https://arxiv.org/abs/2609.39745

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