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Let Spec(A) be an affine derived stack. We give two proofs of the existenceof a canonical map from the moduli space of shifted Poisson structures (in thesense of Pantev-To\"en-Vaqui\'e-Vezzosi, see http://arxiv.org/abs/1111.3209 )on Spec(A) to the moduli space of homotopy (shifted) Poisson algebra structureson A. The first makes use of a more general description of the Poisson operadand of its cofibrant models, while the second in more computational andinvolves an explicit resolution of the Poisson operad.

Poisson bivectors and Poisson brackets on affine derived stacks