Universal Lie Formulas for Higher Antibrackets - Manetti, M.; Ricciardi, G. (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
We prove that the hierarchy of higher antibrackets (aka higher Koszul brackets, aka Koszul braces) of a linear operator Δ on a commutative superalgebra can be defined by some universal formulas involving iterated Nijenhuis-Richardson brackets having as arguments Δ and the multiplication operators. As a byproduct, we can immediately extend higher antibrackets to noncommutative algebras in a way preserving the validity of generalized Jacobi identities.