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.
Universal Lie formulas for higher antibrackets / Manetti, Marco; Ricciardi, Giulia. - In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. - ISSN 1815-0659. - ELETTRONICO. - 12:(2016). [10.3842/SIGMA.2016.053]
Universal Lie formulas for higher antibrackets
MANETTI, Marco
;
2016
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.| File | Dimensione | Formato | |
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Note: https://arxiv.org/abs/1509.09032
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