Universal Lie Formulas for Higher Antibrackets
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. A...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147749 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Universal Lie Formulas for Higher Antibrackets / M. Manetti, G. Ricciardi // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862718997392261120 |
|---|---|
| author | Manetti, M. Ricciardi, G. |
| author_facet | Manetti, M. Ricciardi, G. |
| citation_txt | Universal Lie Formulas for Higher Antibrackets / M. Manetti, G. Ricciardi // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 30 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-12-07T18:18:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147749 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:18:32Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Manetti, M. Ricciardi, G. 2019-02-15T19:08:20Z 2019-02-15T19:08:20Z 2016 Universal Lie Formulas for Higher Antibrackets / M. Manetti, G. Ricciardi // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 30 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B60; 17B70 DOI:10.3842/SIGMA.2016.053 https://nasplib.isofts.kiev.ua/handle/123456789/147749 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Universal Lie Formulas for Higher Antibrackets Article published earlier |
| spellingShingle | Universal Lie Formulas for Higher Antibrackets Manetti, M. Ricciardi, G. |
| title | Universal Lie Formulas for Higher Antibrackets |
| title_full | Universal Lie Formulas for Higher Antibrackets |
| title_fullStr | Universal Lie Formulas for Higher Antibrackets |
| title_full_unstemmed | Universal Lie Formulas for Higher Antibrackets |
| title_short | Universal Lie Formulas for Higher Antibrackets |
| title_sort | universal lie formulas for higher antibrackets |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147749 |
| work_keys_str_mv | AT manettim universallieformulasforhigherantibrackets AT ricciardig universallieformulasforhigherantibrackets |