Shifted Derived Poisson Manifolds Associated with Lie Pairs

Ruggero Bandiera, Zhuo Chen, Mathieu Stiénon, Ping Xu

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We study the shifted analogue of the “Lie–Poisson” construction for L algebroids and we prove that any L algebroid naturally gives rise to shifted derived Poisson manifolds. We also investigate derived Poisson structures from a purely algebraic perspective and, in particular, we establish a homotopy transfer theorem for derived Poisson algebras. As an application, we prove that, given a Lie pair (L, A), the space totΩA∙(Λ∙(L/A)) admits a degree (+ 1) derived Poisson algebra structure with the wedge product as associative multiplication and the Chevalley–Eilenberg differential dABott:ΩA∙(Λ∙(L/A))→ΩA∙+1(Λ∙(L/A)) as unary L bracket. This degree (+ 1) derived Poisson algebra structure on totΩA∙(Λ∙(L/A)) is unique up to an isomorphism having the identity map as first Taylor coefficient. Consequently, the Chevalley–Eilenberg hypercohomology H(totΩA∙(Λ∙(L/A)),dABott) admits a canonical Gerstenhaber algebra structure.

Original languageEnglish (US)
Pages (from-to)1717-1760
Number of pages44
JournalCommunications In Mathematical Physics
Volume375
Issue number3
DOIs
StatePublished - May 1 2020

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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