@article{9ffd762294254058b8858f1754eb253d,
title = "The Berkovits Complex and Semi-free Extensions of Koszul Algebras",
abstract = "In his extension [3] of W. Siegel{\textquoteright}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. ",
author = "Imma Galvez and Vasily Gorbunov and Zain Shaikh and Andrew Tonks",
note = "Acknowledgments. — The first author was partially supported by Spanish Government grants MTM2010-15831, MTM2010-20692, MTM2012-38122- C03-01, MTM2013-42178-P and MTM2015-69135-P and Catalan Government grants SGR1092-2009 and SGR634-2014, and the fourth author by MTM2010-15831 and MTM2013-42178-P. All the authors visited the Max Planck Institute while working on this project and are grateful to the Institute for excellent working conditions. The authors also thank to L.A. Bokut, A. Losev and M. Movshev for very useful discussions and advice, and A. Conca and S. Iyengar for pointing us to Avramov{\textquoteright}s commutative algebra constructions in [2]. We are also grateful to the referee for pointing out an error in [8, Theorem 4.4.1], which we initially used to construct the smaller complex for a larger class of algebras. Of course we also are very grateful to Vadim Schechtman with whom this project originally was started and to whom we dedicate it with our best wishes.",
year = "2016",
doi = "10.5802/afst.1497",
language = "English",
volume = "XXV",
pages = "363--384",
journal = "Annales de la Facult{\'e} des Sciences de Toulouse",
publisher = "Universit{\'e} Paul Sabatier",
number = "2-3",
}