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. - 12:(2016). [10.3842/SIGMA.2016.053]

Universal Lie formulas for higher antibrackets

RICCIARDI, GIULIA
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.
2016
Universal Lie formulas for higher antibrackets / Manetti, Marco; Ricciardi, Giulia. - In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. - ISSN 1815-0659. - 12:(2016). [10.3842/SIGMA.2016.053]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/634804
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