2024/05/16 by Jinbi Zhang, Zhang, Jinbi, Junling Zheng +1
Mathematics · #16E05 #16E10 #16G10 #18G80 #FOS: Mathematics #Fixed Point Theorems Analysis #Nonlinear Differential Equations Analysis #Representation Theory (math.RT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2405.09958
openalex publication_date 2024/05/16 · openalex created_date 2024/05/18 · openalex updated_date 2026/07/28
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.