IASM Preprint Series 2022-02: Commutativity of quantization and reduction for quiver representations


Abstract. Given a finite quiver, its double may be viewed as its non-commutative “cotangent”space, and hence is a non-commutative symplectic space. Crawley-Boevey, Etingof and Ginzburg constructed the non-commutative reduction of this space while Schedler constructed its quantization. We show that the non-commutative quantization and reduction commute with each other. Via the quantum and classical trace maps, such a commutativity induces the commutativity of the quantization and reduction on the space of quiver representations.