Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Zhang, Xiaojin, Zhou, Panyue
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2271735553, G2985936811, G5646081729
OpenAlex ID: W7213424074