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Bibliographic Details
Main Authors: Chang, Hua-Shin, Liao, Hsuan-Yi
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2309.02826
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Table of Contents:
  • 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 $\mathrm{pbw}_2^{-1}\circ \mathrm{pbw}_1$ associated with two Poincaré--Birkhoff--Witt isomorphisms that arise from two choices of a splitting and a connection.