Reference : Pre-Courant algebroids
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Pre-Courant algebroids
Bruce, Andrew mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Grabowski, Janusz mailto [Polish Academy of Sciences > Institute of Mathematics,]
Journal of Geometry and Physics
[en] Courant algebroids ; VB-Courant algebroids ; Q-manifolds
[en] Pre-Courant algebroids are ‘Courant algebroids’ without the Jacobi identity for the Courant–Dorfman bracket. We examine the corresponding supermanifold description of pre-Courant algebroids and some direct consequences thereof. In particular, we define symplectic almost Lie 2-algebroids and show how they correspond to pre-Courant algebroids. We give the definition of (sub-)Dirac structures and study the naïve quasi-cochain complex within the setting of supergeometry. Moreover, the framework of supermanifolds allows us to economically define and work with pre-Courant algebroids equipped with a compatible non-negative grading. VB-Courant algebroids are natural examples of what we call weighted pre-Courant algebroids and our approach drastically simplifies working with them.

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