Poisson bivectors and Poisson brackets on affine derived stacks

Abstract

Let Spec(A) be an affine derived stack. We give two proofs of the existence of a canonical map from the moduli space of shifted Poisson structures (in the sense of Pantev-Toën-Vaquié-Vezzosi, see http://arxiv.org/abs/1111.3209 ) on Spec(A) to the moduli space of homotopy (shifted) Poisson algebra structures on A. The first makes use of a more general description of the Poisson operad and of its cofibrant models, while the second in more computational and involves an explicit resolution of the Poisson operad.

arXiv comment23 pages. Revised argument in section 3, results unchanged