For a local vector bundle V over M, the bundle S^⊠(S^⊗(V)) is the free commutative 2-algebra generated by V, and skew-symmetric maps V ⊠ V to the unit induce compatible Poisson brackets on the resulting equivariant 2-algebra bundle over configuration spaces.
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Equivariant Poisson 2-Algebra Bundles over Configuration Spaces
For a local vector bundle V over M, the bundle S^⊠(S^⊗(V)) is the free commutative 2-algebra generated by V, and skew-symmetric maps V ⊠ V to the unit induce compatible Poisson brackets on the resulting equivariant 2-algebra bundle over configuration spaces.