Bulletin de la Société Royale des Sciences de Liège Bulletin de la Société Royale des Sciences de Liège -  Volume 76 - Année 2007 

About the cohomology of the Lie superalgebra of vector fields on Rn|n

Ammar FAOUZI, 

Université de Sfax, Faculté des Sciences, B.P. 802, Sfax, Tunisie

Kamoun KAOUTHAR, 

faammar@yahoo.com

Abstract

In this paper, we compute the first space of cohomology of Vect(Rn|n), the Lie superalgebra of vector fields on the supermanifold Rnjn with coeffcients in F(Rn|n), the space of smooth functions on Rn|n.  We give a super analog of the cohomologies of vector fields that where studied for instance by D.B. Fuchs

This work allows us to classify the deformations of the action of

Vect(Rn|n) on F(Rn|n).

To cite this article

Ammar FAOUZI & Kamoun KAOUTHAR, «About the cohomology of the Lie superalgebra of vector fields on Rn|n», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 76 - Année 2007, 12-20 URL : http://popups.ulg.be/0037-9565/index.php?id=450.