@Article{Mikulski2020,
author = "Mikulski, Włodzimierz M.",
title = "On the twisted Dorfman-Courant like brackets",
journal = "Opuscula Math.",
year = "2020",
volume = "40",
number = "6",
pages = "703--723",
doi = "https://doi.org/10.7494/OpMath.2020.40.6.703",
url = "https://doi.org/10.7494/OpMath.2020.40.6.703",
abstract = "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.",
keywords = "natural operator, linear vector field, linear form, (twisted) Dorfman-Courant bracket, Jacobi identity in Leibniz form",
issn = "1232-9274"
}