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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2016 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2016
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147749 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Universal Lie Formulas for Higher Antibrackets / M. Manetti, G. Ricciardi // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 30 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147749 |
|---|---|
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Universal Lie Formulas for Higher Antibrackets |
| spellingShingle |
Universal Lie Formulas for Higher Antibrackets Manetti, M. Ricciardi, G. |
| title_short |
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_sort |
universal lie formulas for higher antibrackets |
| author |
Manetti, M. Ricciardi, G. |
| author_facet |
Manetti, M. Ricciardi, G. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147749 |
| 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. |
| work_keys_str_mv |
AT manettim universallieformulasforhigherantibrackets AT ricciardig universallieformulasforhigherantibrackets |
| first_indexed |
2025-12-07T18:18:32Z |
| last_indexed |
2025-12-07T18:18:32Z |
| _version_ |
1850874541010583552 |