Vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair

2023/09/06 by Hua-Shin Chang, Chang, Hua-Shin, Hsuan-Yi Liao +1
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2309.02826

openalex publication_date 2023/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair (L,A), i.e. a pair of a Lie algebroid L and a Lie subalgebroid A of L. The construction of Fedosov dg manifolds involves a choice of a splitting and a connection. We prove that, given any two choices of a splitting and a connection, there exists a unique vertical isomorphism, determined by an iteration formula, between the two associated Fedosov dg manifolds. As an application, we provide an explicit formula for the map pbw₂^-1∘ pbw₁ associated with two Poincaré--Birkhoff--Witt isomorphisms that arise from two choices of a splitting and a connection.

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