Fluxes of Courant Bracket Twisted at the Same Time by B$B$ and θ$\theta$

Abstract The simultaneous twisting of the Courant bracket by a 2‐form and a bi‐vector is investigated, with the generalized fluxes obtained in Courant algebroid relations explored. The twisted Lie bracket is defined and it is demonstrate that the generalized ‐flux can be expressed as the field strength defined on this Lie algebroid. Similarly, it is shown that the ‐flux is a direct consequence of simultaneous twisting, which arises in the twisted Lie bracket relations between holonomic partial derivatives. The generalized flux is obtained in terms of the twisted Koszul bracket, which is identified as a quasi‐Lie algebroid bracket. The action of an exterior derivative related to the twisted Koszul bracket on a bi‐vector produces the generalized ‐flux. It is shown that the generalized ‐flux is also the twisted Schouten–Nijenhuis bracket, i.e., the natural graded bracket on multi‐vectors defined with the twisted Lie bracket.