H-twisted Courant algebroids

TL;DR

This paper generalizes the concept of H-twisted Courant algebroids by allowing the twist to be a closed 4-form in the kernel of the anchor map, and introduces a related cohomology theory.

Contribution

It extends the definition of H-twisted Courant algebroids to include a broader class of twists and develops a new cohomology framework for these structures.

Findings

Defined a generalized H-twisted Courant algebroid with a closed 4-form twist

Provided examples of the generalized structures

Established a cohomology theory for these algebroids

Abstract

We generalize Hansen--Strobl's definition of $H$-twisted Courant algebroid such that the twist $H$ of the Jacobi identity is a 4-form in the kernel of the anchor map and is closed under a naturally occurring exterior covariant derivative. We give examples and define a cohomology.