2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137481We prove that the category of representations of the N-Kronecker quiver and that of coherent sheaves on the noncommutative projective scheme of $R=k< X_1,...,X_N >/(\sum^N_{i=1}X_i^2)$ are derived equivalent. This equivalence is easily proved by applying Orlov's Theorem, on the other hand,in our proof,the quadratic relation $\sum_{i=1}^NX_i^2$ naturally arises from Auslander-Reiten Theory.16 pages. This paper is formerly named "Auslander-Reiten theory and noncommutative projective schemes"Algebraic GeometryRings and Algebras16G70,14A22,16G20text