Formality Theorem and Kontsevich-Duflo Theorem for Lie Pairs
主 题: Formality Theorem and Kontsevich-Duflo Theorem for Lie Pairs
报告人: Ping Xu (Penn State University)
时 间: 2017-06-13 15:15 - 2017-06-13 17:15
地 点: Room 9, Quan Zhai, BICMR
\n\t
\n\t\tA Lie pair (L,A) consists of a Lie algebra (or ?more generally,?a\nLie algebroid) L together with a Lie subalgebra (or Lie subalgebroid) A. A wide\nrange of geometric situations can be described in terms of Lie pairs including\ncomplex manifolds, foliations, and manifolds equipped with Lie group actions. To\neach Lie pair (L,A) are associated two L-infinity algebras, which play roles\nsimilar to the spaces of polyvector fields and polydifferential operators. We\nestablish the formality theorem for Lie pairs. As an application, we obtain Kontsevich-Duflo\ntype theorem for Lie pairs. Besides using Kontsevich formality theorem, our\napproach is based on the construction of a dg manifold (L[1] + L\/A, Q) together\nwith a dg foliation, called the Fedosov dg Lie algebroid. This is a joint work\nwith Hsuan-Yi Liao and Mathieu Stienon.\n\t<\/p>\n
\n<\/div>
