The invariance of the Auslander-Reiten Formula for hereditary algebras
Andrew Hubery
TL;DR
This paper proves that the Auslander-Reiten Formula remains unchanged when applying the Auslander-Reiten translate in the context of finite dimensional hereditary algebras, highlighting a fundamental invariance property.
Contribution
It establishes the invariance of the Auslander-Reiten Formula under the Auslander-Reiten translate for hereditary algebras, a result not previously known.
Findings
The formula is invariant under the Auslander-Reiten translate.
The result applies specifically to finite dimensional hereditary algebras.
This invariance deepens understanding of the structure of these algebras.
Abstract
We show that the Auslander-Reiten Formula for a finite dimensional hereditary algebra is invariant under the Auslander-Reiten translate.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Operator Algebra Research