In his extension  of W. Siegel’s ideas on string quantization, N. Berkovits made several observations which deserve further study and development. Indeed, interesting accounts of this work have already appeared in the mathematical literature [8, 15] and in a different guise due to Avramov. In this paper we bridge between these three approaches, by providing a complex that is useful in the calculation of some homologies.
Galvez, I., Gorbunov, V., Shaikh, Z., & Tonks, A. (2016). The Berkovits Complex and Semi-free Extensions of Koszul Algebras. Annales de la Faculté des Sciences de Toulouse, XXV(2-3), 363-384. https://doi.org/10.5802/afst.1497