Generalized Auslander-Reiten conjecture and derived equivalences
Shengyong Pan
TL;DR
This paper proves that the generalized Auslander-Reiten conjecture remains valid when passing between derived equivalent Artin algebras, highlighting the conjecture's invariance under derived equivalences.
Contribution
It establishes that the generalized Auslander-Reiten conjecture is preserved under derived equivalences between Artin algebras, a new invariance property.
Findings
The conjecture is invariant under derived equivalences.
Derived equivalences preserve the validity of the conjecture.
The result applies to all Artin algebras.
Abstract
In this note, we prove that the generalized Auslander-Reiten conjecture is preserved under derived equivalences between Artin algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra