Commutativity of Quantization and Reduction for Quiver Representations

2021/05/12 by Zhao, Hu
#16G20 #53D55 #81R60 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2105.05440

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.

Related

• Noncommutative Hamiltonian structures and quantizations on preprojective algebras
• Non-commutative Rank and Semi-stability of Quiver Representations
• The monoid of families of quiver representations
• Isomorphisms of quantizations via quantization of resolutions
• Noncommutative compact manifolds constructed from quivers