Bulletin de la Société Royale des Sciences de Liège

0037-9565 1783-5720

 

sinds 05 februari 2011 :
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B. Agrebaoui & N. Ben Fraj

On the cohomology of the Lie Superalgebra of contact vector fields on S1/1

(Volume 73 - Année 2004 — Numéro 5 - 6)
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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 K(l) of contact vector fields on the supercircle S1/1 in the Lie Superalgebra of superpseudodifferential operators.  Following the paper of V. Ovsienko and C. Roger, Deforming the Lie algebra of vector fields on SI inside the Poisson algebra on T*S1, Comm. Math. Phys., 198 (1998) 97-110, we show that this space is four-dimensional with only even cocycles and we calculate explicitly four l-cocycles representing non-trivial generating cohomology classes.

Om dit artikel te citeren:

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], Volume 73 - Année 2004, Numéro 5 - 6, 365-375 URL : https://popups.uliege.be/0037-9565/index.php?id=389.

Over : B. Agrebaoui

Département de Mathématiques, Faculté des Sciences de Sfax, route de Soukra, 3018 Sfax BP 802, Tunisie, E-mail address : bagreba@fss.rnu.tn

Over : N. Ben Fraj

Institut Supérieur de Sciences Appliquées et Technologie, Sousse, E-mail address: benfraj_nizar@yahoo.fr