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Braces and Poisson additivity
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 8 / August 2018
- Published online by Cambridge University Press:
- 18 July 2018, pp. 1698-1745
- Print publication:
- August 2018
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- Article
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We relate the brace construction introduced by Calaque and Willwacher to an additivity functor. That is, we construct a functor from brace algebras associated to an operad
${\mathcal{O}}$ to associative algebras in the category of homotopy 
${\mathcal{O}}$-algebras. As an example, we identify the category of 
$\mathbb{P}_{n+1}$-algebras with the category of associative algebras in 
$\mathbb{P}_{n}$-algebras. We also show that under this identification there is an equivalence of two definitions of derived coisotropic structures in the literature.
