Triangulated Categories of Gorenstein Cyclic Quotient Singularities

We prove there is an equivalence of derived categories between Orlov’s triangulated category of singularities for a Gorenstein cyclic quotient singularity and the derived category of representations of a quiver with relations, which is obtained from a McKay quiver by removing one vertex and half of the arrows. This result produces examples of distinct quivers with relations which have equivalent derived categories of representations. Fix an integer n greater than one. For a finite subgroupG ofGLn(C), let {ρi} i=0 be the set of irreducible representations of G. Further, let ρNat be the natural n-dimensional representation of G given by the inclusion. For k, l = 0, . . . , N − 1, define the natural numbers akl by the decomposition ρl ⊗ ρNat = ⊕