Fedosov dg manifolds associated with Lie pairs
Fedosov dg manifolds associated with Lie pairs
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DOI：
10.1007/s00208-020-02012-6
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发表时间：
2016-05
影响因子：
1.4
通讯作者：
Mathieu Sti'enon;P. Xu
中科院分区：
文献类型：
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作者：
Mathieu Sti'enon;P. Xu
给定任意李代数对（L，A），构造一个微分梯度流形，称为Fedosov流形。我们证明了仅用Fedosov迭代法构造的同构向量场q是在[18]中建立的poincar<s:1> - birkhoff - witt映射的副产物。最后，利用同调摄动引理，建立了Dolgushev-Fedosov型的拟同构：dg流形上函数的微分梯度代数是同伦等价的。
Given any pair (L,A) of Lie algebroids, we construct a differential graded manifold, which we call Fedosov dg manifold. We prove that the homological vector fieldQconstructed onby the Fedosov iteration method arises as a byproduct of the Poincaré–Birkhoff–Witt map established in [18]. Finally, using the homological perturbation lemma, we establish a quasi-isomorphism of Dolgushev–Fedosov type: the differential graded algebras of functions on the dg manifoldsandare homotopy equivalent.