Second cohomology space of V ect(R) acting on the space of bilinear bidifferential operators, vanishing on sl(2)

Document Type : Research Articles

Authors

1 Faculty of sciences of Gafsa

2 Département de Mathématiques, Faculté des Sciences de Sfax, BP 802, Sfax 3038, Tunisie.

3 Laboratoire de Mathématiques et Modélisation d’Evry, Univ d’Evry, Université Paris Saclay, France.

4 Faculte des sciences de Gafsa , zarroug 2112, Tunisa

10.22080/cjms.2025.27595.1710

Abstract

We consider the V ect(R)-module structure on the spaces of bilinear bidi erential operators
acting on the spaces of weighted densities. We compute the second relative cohomology
group of the Lie algebra V ect(R) with coecients in the space of bilinear bidi erential
operators that act on tensor densities D;;, vanishing on the Lie algebra sl(2).
This work is the simplest generalization of a result by Basdouri et al. [ Second coho-
mology space of sl(2) acting on the space of bilinear bidi erential operators], Journal
Revista de la Union Matematica Argentina (2020).

Keywords

Main Subjects

Files

Share

How to cite

Statistics