Classification of 𝔞𝔣𝔣(3|1)-invariant binary differential operators on weighted densities and cohomology

Author:

Omri Salem1,Swilah Wissal2

Affiliation:

1. Département de Mathématiques, Faculté des Sciences de Gafsa, Université de Gafsa, Zarroug, 2112 Gafsa, Tunisie

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

Abstract

In this paper, we consider the [Formula: see text]-module structure on the spaces of differential bilinear operators acting on the superspaces of weighted densities. We classify [Formula: see text]-invariant binary differential operators acting on the spaces of weighted densities. This result allows us to compute the first [Formula: see text]-relative differential cohomology of [Formula: see text] with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities. Finally, we deduce the classification of the [Formula: see text]-relative extension of [Formula: see text] modules [Formula: see text]

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

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