Igusa-Todorov distances

Jinbi Zhang; Junling Zheng

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arXiv · 2405.09958

Igusa-Todorov distances

Jinbi Zhang·Junling Zheng

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Abstract

A new homological dimension, called the Igusa-Todorov distance, is introduced to measure how far an Artin algebra is from being an Igusa-Todorov algebra. An upper bound for the dimension is established in terms of the Loewy length, leading to the conclusion that every Artin algebra has a finite Igusa-Todorov distance.Using this dimension, we derive an upper bound for the dimension of the singularity category. Furthermore, we investigate how the Igusa-Todorov distance behaves under various relationships between algebras. Specifically, we demonstrate that stable equivalences preserve the Igusa-Todorov distances for algebras without nodes, prove that it is an invariant under singular equivalence of Morita type with level, and establish bounds for the distances of algebras involved in a recollement of derived module categories. Consequently, the Igusa-Todorov distance is an invariant under derived equivalences of algebras.

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BibTeX RIS

Jinbi Zhang, Junling Zheng. 2024-05-16. Igusa-Todorov distances. https://arxiv.org/abs/2405.09958

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