For every d at least 2, the full Kontsevich graph complex maps injectively into the Chevalley-Eilenberg complex of the n=d-1 Schouten algebra, so its zeroth cohomology acts via L-infinity automorphisms on graded symplectic manifolds.
A Formality quasi-isomorphism for Hochschild cochains over rationals can be constructed recursively
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It is believed arXiv:0808.2762, arXiv:math/9904055 that, among the coefficients entering Kontsevich's formality quasi-isomorphism arXiv:q-alg/9709040, there are irrational (possibly even transcendental) numbers. In this paper, we prove that a formality quasi-isomorphism for Hochschild cochains of a polynomial algebra over rationals can be constructed recursively. The proof that the proposed recursive algorithm works, is based on the existence of formality quasi-isomorphism over reals. However, the algorithm requires no explicit knowledge of the coefficients entering Kontsevich's construction. Although this algorithm completely bypasses Tamarkin's approach arXiv:math/0003052, arXiv:math/9803025, the construction is inspired by Proposition 5.8 from the classical paper (Algebra i Analiz, 1990) by V. Drinfeld.
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M. Kontsevich's graph complexes and universal structures on graded symplectic manifolds
For every d at least 2, the full Kontsevich graph complex maps injectively into the Chevalley-Eilenberg complex of the n=d-1 Schouten algebra, so its zeroth cohomology acts via L-infinity automorphisms on graded symplectic manifolds.