A noncommutative version of Beilinson's Theorem

Abstract

We prove that the category of representations of the N-Kronecker quiver and that of coherent sheaves on the noncommutative projective scheme of $R=k<X_1,...,X_N>/({\sum }_{i=1}^N{X}_i^2)$ are derived equivalent. This equivalence is easily proved by applying Orlov's Theorem, on the other hand,in our proof,the quadratic relation ${\sum }_{i=1}^N{X}_i^2$ naturally arises from Auslander-Reiten Theory.

16 pages. This paper is formerly named "Auslander-Reiten theory and noncommutative projective schemes"