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Hamiltonian reduction and Maurer-Cartan equations

2003/04/20 by Wee Liang Gan, Victor Ginzburg, Gan, Wee Liang +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #math.AG #math.QA #math.SG

paper · pdf · doi:10.48550/arxiv.math/0304276

9 pp., expanded version: more details and comments added

openalex publication_date 2003/04/20 · arxiv created 2003/11/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that solving the Maurer-Cartan equations is, essentially, the same thing as performing the Hamiltonian reduction construction. In particular, any differential graded Lie algebra equipped with an even nondegenerate invariant bilinear form gives rise to modular stacks with symplectic structures.

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