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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\nu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ν</mi> </math></EquationSource> </InlineEquation>-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.</p>

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New invariants of stable equivalences and Auslander–Reiten conjecture

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • Changchang Xi,
  • Jinbi Zhang

摘要

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 \(\nu \) 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.