$\mathfrak{sl}(2)$-cohomology on multidifferential operators space

Didier Arnal; Mabrouk Ben Ammar

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arXiv · 2311.09199

$\mathfrak{sl}(2)$-cohomology on multidifferential operators space

Didier Arnal·Mabrouk Ben Ammar

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Abstract

In this paper, we consider the known question of the computation of the cohomology spaces for the natural action of the Lie algebra $\mathfrak{sl}(2)$ acting on the space $\Dlm$ of multidifferential operators on the line. We first show that these cohomology spaces are entirely characterized by a linear map $f$ between two explicit finite dimensional spaces, then we prove that this map has always maximal rank, allowing to get explicit recursive expression for their dimensions.

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BibTeX RIS

Didier Arnal, Mabrouk Ben Ammar. 2023-11-15. $\mathfrak{sl}(2)$-cohomology on multidifferential operators space. https://arxiv.org/abs/2311.09199

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