2022/07/22 by Changchang Xi, Xi, Changchang, Jinbi Zhang +1
Mathematics · #15A27 #16E05 #16L60 #18G80 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 16G10 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #Secondary 16D60
paper · pdf · doi:10.48550/arxiv.2207.10848
openalex publication_date 2022/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that stable equivalences between Artin algebras without nodes preserve homological data that provide upper bounds for finitistic dimension, and that stable equivalences between Artin algebras with positive ν-dominant dimensions induce stable equivalences of their Frobenius parts. As an application of our new methods developed, we verify the Auslander--Reiten conjecture on stable equivalences for two rather different classes of algebras: principal centralizer matrix algebras over arbitrary fields and Frobenius-finite algebras over algebraically closed fields.