Preprojective algebras were first defined by Gel’fand and Ponomarev to study the representation theory of algebras of global dimension 1. They were later generalized by Iyama to algebras of higher global dimensions. In the classical case, preprojective algebras play an important role as bridges between singularity theory and non-commutative algebraic geometry. In fact, if we let G be a finite subgroup of SL(2,k), Reiten and Van den Bergh showed that the so called skew-group algebra, associated to the quotient singularity k^2/G, is Morita equivalent to a preprojective algebra. It is then interesting to ask for which finite subgroup G < SL(n,k) is the skew-group algebra Morita equivalent to an higher preprojective algebra. When G is cyclic and satisfies an extra condition, Amiot, Iyama and Reiten proved that the skew-group algebra is a preprojective algebra. In this talk, we will give a converse to this theorem, and generalize it to any finite subgroups of SL(n,k). We will also explain the important background notions.