Braces and Poisson additivity

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 $O$ to associative algebras in the category of homotopy $O$-algebras. As an example, we identify the category of $P_{n+1}$-algebras with the category of associative algebras in $P_n$-algebras. We also show that under this identification there is an equivalence of two definitions of derived coisotropic structures in the literature.

49 pages

References in corpus (1)

• Derived coisotropic structures I: affine case

Cited by in corpus (14)

• Derived coisotropic structures II: stacks and quantization
• Derived coisotropic structures I: affine case
• Graded Poisson Algebras
• Poisson vertex algebras in supersymmetric field theories
• Shifted Coisotropic Correspondences
• Quantisation of derived Lagrangians
• Factorization Algebras for Bulk-Boundary Systems
• On Quantum Obstruction Spaces and Higher Codimension Gauge Theories
• A holography theory of Poisson sigma model and deformation quantization
• Deformation Quantization via Categorical Factorization Homology
• Exact triangles, Koszul duality, and coisotopic boundary conditions
• Algebras over not too little discs
• A Physical Origin for Singular Support Conditions in Geometric Langlands Theory
• Cohomological invariants of algebraic operads, I