Universal Lie Formulas for Higher Antibrackets

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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dc.contributor.author	Manetti, M.
dc.contributor.author	Ricciardi, G.
dc.date.accessioned	2019-02-15T19:08:20Z
dc.date.available	2019-02-15T19:08:20Z
dc.date.issued	2016
dc.identifier.citation	Universal Lie Formulas for Higher Antibrackets / M. Manetti, G. Ricciardi // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 30 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 17B60; 17B70
dc.identifier.other	DOI:10.3842/SIGMA.2016.053
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147749
dc.description.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.	uk_UA
dc.description.sponsorship	We thank Bruno Vallette for useful comments and for bringing to our attention the pre-Lie Magnus expansion. We are indebted with the anonymous referees for several remarks and especially for letting us into the knowledge of the papers [3, 28]. M.M. acknowledges partial support by Italian MIUR under PRIN project 2012KNL88Y “Spazi di moduli e teoria di Lie”; G.R. acknowledges partial support by Italian MIUR under PRIN project 2010YJ2NYW and INFN under specific initiative QNP.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Universal Lie Formulas for Higher Antibrackets	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA