Noncommutative Hamiltonian structures and quantizations on preprojective algebras

2023/12/29 by Hu Zhao, Zhao, Hu
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2312.17578

Abstract

Given a noncommutative Hamiltonian space A, we prove that the conjecture ``\it quantization commutes with reduction'' holds for A. We further construct a semidirect product algebra A \rtimes \mG^A, and establish a correspondence between equivariant sheaves on the representation space and left A\rtimes\mG^A-modules. In the quiver setting, using the quantum and classical trace maps, we establish the explicit correspondence between quantizations of a preprojective algebra and those of a quiver variety.

Related

• Commutativity of Quantization and Reduction for Quiver Representations
• Isomorphisms of quantizations via quantization of resolutions
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• Noncommutative geometry and quantization
• Noncommutative Geometry and Quiver algebras