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Fedosov dg manifolds associated with Lie pairs
Mathematische Annalen ( IF 1.3 ) Pub Date : 2020-07-26 , DOI: 10.1007/s00208-020-02012-6
Mathieu Stiénon , Ping Xu

Given any pair $(L,A)$ of Lie algebroids, we construct a differential graded manifold $(L[1]\oplus L/A,Q)$, which we call Fedosov dg manifold. We prove that the cohomological vector field $Q$ constructed on $L[1]\oplus L/A$ by the Fedosov iteration method arises as a byproduct of the Poincare--Birkhoff--Witt map established in arXiv:1408.2903. Finally, using the homological perturbation lemma, we establish a quasi-isomorphism of Dolgushev--Fedosov type: the differential graded algebras of functions on the dg manifolds $(A[1],d_A)$ and $(L[1]\oplus L/A,Q)$ are homotopy equivalent.

中文翻译:

与李对相关的 Fedosov dg 流形

给定任何一对 $(L,A)$ 的李代数体,我们构造一个微分分级流形 $(L[1]\oplus L/A,Q)$,我们称之为 Fedosov dg 流形。我们证明了通过 Fedosov 迭代方法在 $L[1]\oplus L/A$ 上构建的上同调向量场 $Q$ 是 arXiv:1408.2903 中建立的 Poincare--Birkhoff--Witt 映射的副产品。最后,利用同调微扰引理,我们建立了 Dolgushev--Fedosov 型的拟同构:dg 流形上函数的微分分级代数 $(A[1],d_A)$ 和 $(L[1]\oplus L/A,Q)$ 是同伦等价的。
更新日期:2020-07-26
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