Polyvector fields and polydifferential operators associated with Lie pairs

Ruggero Bandiera, Mathieu Stiénon, Ping Xu

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Abstract

We prove that the spaces tot (Γ(λA)⊗Rtpolly;) and tot (Γ(λA)⊗RDpolly;) associated with a Lie pair (L,A) each carry an Lalgebra structure canonical up to an L1 isomorphism with the identity map as linear part. These two spaces serve, respectively, as replacements for the spaces of formal polyvector fields and formal polydifferential operators on the Lie pair (L,A). Consequently, both HCE(A tpolly;) and HCE(A Dpolly;) admit unique Gerstenhaber algebra structures. Our approach is based on homotopy transfer and the construction of a Fedosov dg Lie algebroid (i.e. a dg foliation on a Fedosov dg manifold).

Original languageEnglish (US)
Pages (from-to)643-711
Number of pages69
JournalJournal of Noncommutative Geometry
Volume15
Issue number2
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Mathematical Physics
  • Geometry and Topology

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