Let (M,ω) be a symplectic manifold. Poisson brackets of the exterior forms are defined by the following formulas:
{α,{β,γ}}={{α,β},γ}+{β,{α,γ}}
{α,β}=(−1)deg(α)deg(β)+1{β,α}
{fα,β}=α∧∇Xfβ+f{α,β}
with α,β,γ∈Λ∗(TM) and f∈C∞(M), Xf=(df)∗. ∇ is a symplectic connection.
Can we quantize the structure?