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B. Agrebaoui & N. Ben Fraj

ON THE COHOMOLOGY OF THE LIE SUPERALGEBRA OF CONTACT VECTOR FIELDS ON S1/1

(Volume 72 - Année 2003 — Numéro 6)
Article
Open Access
Mots-clés : pseudodifferentiel operator, super cercle, cohomology, contact vector fields

Abstract

We investigate the first cohomology space attached to the embedding of the Lie superalgebra S(1/1) of contact vector fields on the supercircle in the Lie Superalgebra of superpseudodifferential operators.  We show that this space is four-dimensional with only even cocycles and we calculate explicitly four 1-cocycles representing non-trivial generating cohomology classes.

To cite this article

B. Agrebaoui & N. Ben Fraj, «ON THE COHOMOLOGY OF THE LIE SUPERALGEBRA OF CONTACT VECTOR FIELDS ON S1/1», Bulletin de la Société Royale des Sciences de Liège [En ligne], Numéro 6, Volume 72 - Année 2003, 365 - 375 URL : https://popups.uliege.be/0037-9565/index.php?id=945.

About: B. Agrebaoui

Département de Mathématiques, Faculté des Sciences de Sfax, Route de Soukra,,3018 Sfax BP 802, Tunisie, bagreba@fss.rnu.tn

About: N. Ben Fraj

Institut Supérieur de Sciences Appliquées et Technologie, Sousse, benfraj-nizar@yahoo.fr