# 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…

## 17 Citations

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We prove that the spaces $\operatorname{tot}\big(\Gamma(\Lambda^\bullet A^\vee \otimes_R\mathcal{T}_{\operatorname{poly}}^{\bullet}\big)$ and $\operatorname{tot}\big(\Gamma(\Lambda^\bullet…

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