Shifted Derived Poisson Manifolds Associated with Lie Pairs

@article{Bandiera2019ShiftedDP,
  title={Shifted Derived Poisson Manifolds Associated with Lie Pairs},
  author={Ruggero Bandiera and Zhuo Chen and Mathieu Sti{\'e}non and Ping Xu},
  journal={Communications in Mathematical Physics},
  year={2019},
  volume={375},
  pages={1717-1760}
}
We study the shifted analogue of the “Lie–Poisson” construction for $$L_\infty $$ L ∞ algebroids and we prove that any $$L_\infty $$ 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 $$\hbox {tot}\Omega ^{\bullet }_A(\Lambda… 
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