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On the gauge-natural operators similar to the twisted Dorfman-Courant bracket

Mikulski Włodzimierz M.

Opuscula Mathematica

2021

Vol. 41, no. 2

205--226

All [formula]-gauge-natural operators C sending linear 3-forms [formula] on a smooth [formula] vector bundle E into R-bilinear operators [formula] transforming pairs of linear sections of [formula] into linear sections of [formula] are completely described. The complete descriptions is given of all generalized twisted Dorfman-Courant brackets C (i.e. C as above such that C0 is the Dorfman-Courant bracket) satisfying the Jacobi identity for closed linear 3-forms H . An interesting natural characterization of the (usual) twisted Dorfman-Courant bracket is presented.

On the twisted Dorfman-Courant like brackets

Mikulski Włodzimierz M.

Opuscula Mathematica

2020

Vol. 40, no. 6

703--723

There are completely described all [formula]-gauge-natural operators C which, like to the Dorfman-Courant bracket, send closed linear 3-forms [formula]on a smooth (C ∞) vector bundle E into R-bilinear operators [formula] transforming pairs of linear sections of [formula] into linear sections of [formula]. 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.