On the twisted Dorfman-Courant like brackets
There are completely described all \(\mathcal{VB}_{m,n}\)-gauge-natural operators \(C\) which, like to the Dorfman-Courant bracket, send closed linear \(3\)-forms \(H\in\Gamma^{l-\rm{clos}}_E(\bigwedge^3T^*E)\) on a smooth (\(\mathcal{C}^{\infty}\)) vector bundle \(E\) into \(\mathbf{R}\)-bilinear o...
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AGH Univeristy of Science and Technology Press
2020-12-01
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| Series: | Opuscula Mathematica |
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| Online Access: | https://www.opuscula.agh.edu.pl/vol40/6/art/opuscula_math_4039.pdf |
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doaj-fdd47dccf2e0469d9b2b2f1c8c538a8d2021-02-08T18:34:28ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742020-12-01406703723https://doi.org/10.7494/OpMath.2020.40.6.7034039On the twisted Dorfman-Courant like bracketsWłodzimierz M. Mikulski0https://orcid.org/0000-0002-2905-0461Jagiellonian University, Department of Mathematics, S. Łojasiewicza 6, Cracow, PolandThere are completely described all \(\mathcal{VB}_{m,n}\)-gauge-natural operators \(C\) which, like to the Dorfman-Courant bracket, send closed linear \(3\)-forms \(H\in\Gamma^{l-\rm{clos}}_E(\bigwedge^3T^*E)\) on a smooth (\(\mathcal{C}^{\infty}\)) vector bundle \(E\) into \(\mathbf{R}\)-bilinear operators \[C_H:\Gamma^l_E(TE\oplus T^*E)\times \Gamma^l_E(TE\oplus T^*E)\to \Gamma^l_E(TE\oplus T^*E)\] transforming pairs of linear sections of \(TE\oplus T^*E\to E\) into linear sections of \(TE\oplus T^*E\to E\). Then all such \(C\) which also, like to the twisted Dorfman-Courant bracket, satisfy both some "restricted" condition and the Jacobi identity in Leibniz form are extracted.https://www.opuscula.agh.edu.pl/vol40/6/art/opuscula_math_4039.pdfnatural operatorlinear vector fieldlinear form(twisted) dorfman-courant bracketjacobi identity in leibniz form |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Włodzimierz M. Mikulski |
| spellingShingle |
Włodzimierz M. Mikulski On the twisted Dorfman-Courant like brackets Opuscula Mathematica natural operator linear vector field linear form (twisted) dorfman-courant bracket jacobi identity in leibniz form |
| author_facet |
Włodzimierz M. Mikulski |
| author_sort |
Włodzimierz M. Mikulski |
| title |
On the twisted Dorfman-Courant like brackets |
| title_short |
On the twisted Dorfman-Courant like brackets |
| title_full |
On the twisted Dorfman-Courant like brackets |
| title_fullStr |
On the twisted Dorfman-Courant like brackets |
| title_full_unstemmed |
On the twisted Dorfman-Courant like brackets |
| title_sort |
on the twisted dorfman-courant like brackets |
| publisher |
AGH Univeristy of Science and Technology Press |
| series |
Opuscula Mathematica |
| issn |
1232-9274 |
| publishDate |
2020-12-01 |
| description |
There are completely described all \(\mathcal{VB}_{m,n}\)-gauge-natural operators \(C\) which, like to the Dorfman-Courant bracket, send closed linear \(3\)-forms \(H\in\Gamma^{l-\rm{clos}}_E(\bigwedge^3T^*E)\) on a smooth (\(\mathcal{C}^{\infty}\)) vector bundle \(E\) into \(\mathbf{R}\)-bilinear operators \[C_H:\Gamma^l_E(TE\oplus T^*E)\times \Gamma^l_E(TE\oplus T^*E)\to \Gamma^l_E(TE\oplus T^*E)\] transforming pairs of linear sections of \(TE\oplus T^*E\to E\) into linear sections of \(TE\oplus T^*E\to E\). Then all such \(C\) which also, like to the twisted Dorfman-Courant bracket, satisfy both some "restricted" condition and the Jacobi identity in Leibniz form are extracted. |
| topic |
natural operator linear vector field linear form (twisted) dorfman-courant bracket jacobi identity in leibniz form |
| url |
https://www.opuscula.agh.edu.pl/vol40/6/art/opuscula_math_4039.pdf |
| work_keys_str_mv |
AT włodzimierzmmikulski onthetwisteddorfmancourantlikebrackets |
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1724279643578564608 |