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The Berkovits Complex and Semi-free Extensions of Koszul Algebras
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 2-3, pp. 363-384.

En étendant des idées de W.Siegel sur la quantisation des cordes, N. Berkovits [3] a fait quelques remarques qui méritent d’être étudiées et développées. En fait, des rapports intéressants sur ce travail sont déjà parus dans la littérature mathématique [8, 15], liés aussi à une contruction due à L. Avramov. Dans cet article, on tend des ponts entre ces trois approches, en utilisant la construction d’un complexe approprié au calcul de certains groupes d’homologie.

In his extension [3] 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 L. Avramov. In this paper we bridge between these three approaches, by providing a complex that is useful in the calculation of some homologies.

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     author = {Imma G\'alvez and Vassily Gorbounov and Zain Shaikh and Andrew Tonks},
     title = {The {Berkovits} {Complex} and {Semi-free} {Extensions} of {Koszul} {Algebras}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {363--384},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 25},
     number = {2-3},
     year = {2016},
     doi = {10.5802/afst.1497},
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Imma Gálvez; Vassily Gorbounov; Zain Shaikh; Andrew Tonks. The Berkovits Complex and Semi-free Extensions of Koszul Algebras. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 2-3, pp. 363-384. doi : 10.5802/afst.1497. https://afst.centre-mersenne.org/articles/10.5802/afst.1497/

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