On the structure of graded symplectic supermanifolds and Courant algebroids

@article{Roytenberg2002OnTS,
  title={On the structure of graded symplectic supermanifolds and Courant algebroids},
  author={Dmitry Roytenberg},
  journal={arXiv: Symplectic Geometry},
  year={2002}
}
This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles (E\to M_{0}) by canonically associating to such a bundle a graded symplectic supermanifold ((M,\Omega)), with (\textrm{deg}(\Omega)=2). Conversely, every such manifold arises in this way. We describe the algebra of functions on (M) in terms of (E) and show that ``BRST charges'' on (M) correspond to… 

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