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There is a canonical mapping from the space of sections of the bundle ΛT * M ST M to Ω(T * M; T(T * M)). It is shown that this is a homomorphism on Ω(M; T M) for the Frolicher-Nijenhuis brackets, and also on Γ(ST M) for the Schouten bracket of symmetric multivector fields. But the whole image is not a subalgebra for the Frolicher-Nijenhuis bracket on Ω(T * M; T(T...
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