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Braces and Poisson additivity

Part of: Categories with structure Homological algebra

Published online by Cambridge University Press:  18 July 2018

Pavel Safronov
Pavel Safronov*
Affiliation:
Max-Planck-Institut für Mathematik, Bonn, Germany email psafronov@mpim-bonn.mpg.de
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Abstract

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.

Keywords

operadsKoszul dualityshifted Poisson structures

MSC classification

Primary: 18D50: Operads
Secondary: 18G55: Homotopical algebra
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 8 , August 2018 , pp. 1698 - 1745
Copyright
© The Author 2018 

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Footnotes

1

Current address: Intitut für Mathematik, Winterthurerstrasse 190, 8057 Zürich, Switzerland

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