Commutativity of Quantization and Reduction for Quiver Representations

Hu Zhao

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arXiv · 2105.05440

Commutativity of Quantization and Reduction for Quiver Representations

Hu Zhao

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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.

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Hu Zhao. 2021-05-12. Commutativity of Quantization and Reduction for Quiver Representations. https://arxiv.org/abs/2105.05440

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