TY - JOUR
T1 - Fedosov dg manifolds associated with Lie pairs
AU - Stiénon, Mathieu
AU - Xu, Ping
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - Given any pair (L, A) of Lie algebroids, we construct a differential graded manifold (L[1] ⊕ L/ A, Q) , which we call Fedosov dg manifold. We prove that the homological vector field Q constructed on L[1] ⊕ L/ A by 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 manifolds (A[1] , dA) and (L[1] ⊕ L/ A, Q) are homotopy equivalent.
AB - Given any pair (L, A) of Lie algebroids, we construct a differential graded manifold (L[1] ⊕ L/ A, Q) , which we call Fedosov dg manifold. We prove that the homological vector field Q constructed on L[1] ⊕ L/ A by 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 manifolds (A[1] , dA) and (L[1] ⊕ L/ A, Q) are homotopy equivalent.
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U2 - 10.1007/s00208-020-02012-6
DO - 10.1007/s00208-020-02012-6
M3 - Article
AN - SCOPUS:85088641386
SN - 0025-5831
VL - 378
SP - 729
EP - 762
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1-2
ER -