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arXiv · 2609.14453

Igusa--Todorov Algebras and the Auslander--Reiten Conjecture

Xiaojin Zhang·Panyue Zhou
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Abstract

We prove that every Igusa--Todorov Artin algebra satisfies the Auslander--Reiten conjecture. More precisely, let $V$ be an $n$-Igusa--Todorov witness, and let $t$ be the number of isomorphism classes of nonprojective indecomposable summands of $V$. If a finitely generated module $M$ satisfies $\Ext_A^i(M,A)=0$ for every $i>0$ and $\Ext_A^q(M,M)=0$ for $1\leq q\leq 2t+1$, then $M$ is projective. As applications, algebras of representation dimension at most three and algebras satisfying $J^{2m+1}=0$ for which $A/J^m$ has finite representation type satisfy the Auslander--Reiten conjecture.

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Xiaojin Zhang, Panyue Zhou. 2026-09-15. Igusa--Todorov Algebras and the Auslander--Reiten Conjecture. https://arxiv.org/abs/2609.14453

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