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arXiv · 1509.09032

Universal Lie Formulas for Higher Antibrackets

Marco Manetti·Giulia Ricciardi
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Abstract

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.

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BibTeXRIS

Marco Manetti, Giulia Ricciardi. 2016-06-06. Universal Lie Formulas for Higher Antibrackets. https://doi.org/10.3842/sigma.2016.053

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