A noncommutative version of Beilinsonʹs theorem

We prove that the category of representations of the N-Kronecker quiver is derived equivalent to the category which is considered as the category of coherent sheaves on the noncommutative projective scheme associated to . This theorem is easily proved by applying Orlovʹs theorem. On the other hand, in our proof, a method of noncommutative projective geometry is used, and the quadratic relation naturally arises from Auslander–Reiten theory.