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$𝔰 𝔩 (2, ℝ)$ -invariant $3$ -ary differential operators and cohomology of $𝔰 𝔩 (2, ℝ)$ acting on $3$ -ary differential operators

Basdouri Okba

Laboratoire Algebra Geometry and Theory Spectral Sfax, Tunisie

Département de Mathématiques Faculté des Sciences de Gafsa 2112, Universié de Gafsa, Tunisie

E-mail Address: okbabasdouri1@yahoo.fr

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and

Nasri Elamine

Laboratoire Algebra Geometry and Theory Spectral Sfax, Tunisie

Département de Mathématiques Faculté des Sciences de Gafsa 2112, Universié de Gafsa, Tunisie

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https://doi.org/10.1142/S0219887817500153Cited by:1 (Source: Crossref)

Abstract

We consider the $𝔰 𝔩 (2, ℝ)$ -module structure on the spaces of $3$ -ary differential operators acting on the spaces of weighted densities. We classify $𝔰 𝔩 (2, ℝ)$ -invariant $3$ -ary differential operators. This result allows us to compute the first differential cohomology of the Lie algebra $𝔰 𝔩 (2, ℝ)$ with coefficients in the space of trilinear differential operators.

Keywords:

AMSC: 17B56, 53D55, 58H15

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