Second cohomology space of \frak sl(2) acting on the space of n-ary differential operators on ℝ

2023/11/15 by Mabrouk Ben Ammar, Ammar, Mabrouk Ben
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2311.09199

openalex publication_date 2023/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the spaces F_μ of polynomial μ-densities on the line as \mathfraksl(2)-modules and then we compute the cohomological spaces H²_diff(\mathfraksl(2), D_λ,μ), where μ∈ ℝ, λ=(λ₁,…,λ_n) ∈ℝⁿ and D_λ,μ is the space of n-ary differential operators from F_λ1⊗⋯⊗ F_λn to F_μ.

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