# Pure Spinors on Lie groups

@article{Alekseev2007PureSO, title={Pure Spinors on Lie groups}, author={A. Alekseev and Henrique Bursztyn and Eckhard Meinrenken}, journal={arXiv: Differential Geometry}, year={2007} }

For any manifold M, the direct sum TM \oplus T*M carries a natural inner product given by the pairing of vectors and covectors. Differential forms on M may be viewed as spinors for the corresponding Clifford bundle, and in particular there is a notion of \emph{pure spinor}.
In this paper, we study pure spinors and Dirac structures in the case when M=G is a Lie group with a bi-invariant pseudo-Riemannian metric, e.g. G semi-simple. The applications of our theory include the construction of…

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