Séminaire de Géométrie et Quantification

Ping Xu

(Penn State)

Lundi 29 mai à 15h30, salle 01, IHP

Title:  Formality theorem and  Kontsevich-Duflo theorem for Lie pairs

Résumé:  A Lie pair (L,A) consists of a Lie algebra (or  more generally, a Lie algebroid) L together with a Lie  subalgebra  (or Lie subalgebroid) A. A wide range of geometric situations can be  described in  terms of Lie pairs including complex manifolds, foliations, and  manifolds equipped with Lie group actions.  To each Lie pair (L,A) are associated two L-infinity algebras, which play roles similar to the spaces of polyvector fields and polydifferential operators.  We establish the formality theorem for Lie pairs.

As an application, we obtain  Kontsevich-Duflo type theorem for Lie pairs. Besides using Kontsevich formality theorem, our approach is based on the construction of a dg manifold (L[1] + L/A, Q) together with a  dg foliation, called the Fedosov dg Lie algebroid. This is a joint work with Hsuan-Yi Liao and Mathieu Stiénon

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