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This paper considers the Free Differential Algebra and rheonomicparametrization of type IIA Supergravity, extended to include the BRSdifferential and the ghosts. We consider not only the ghosts lambda's ofsupersymmetry but also the ghosts corresponding to gauge and Lorentztransformations. In this way we can derive not only the BRS transformations offields and ghosts but also the standard pure spinor constraints on lambda's.Moreover the formalism allows to derive the action for the pure spinorformulation of type IIA superstrings in a general background, recovering theaction first obtained by Berkovits and Howe.

Pure Spinor Approach to Type IIA Superstring Sigma Models and Free Differential Algebras