Cohomology of \mathfrak aff(1) and \mathfrak aff(1|1) acting on the space of n-ary differential operators on the superspace ℝ^1|1

2016/04/28 by Mabrouk Ben Ammar, Ammar, Mabrouk Ben, Maha Boujelben +5
Mathematics · #17B10 #17B56 #17B66 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B10 #msc:17B56 #msc:17B66

paper · pdf · doi:10.48550/arxiv.1604.08325

14 pages. arXiv admin note: text overlap with arXiv:0911.2769, arXiv:1512.02847

arxiv created 2016/05/22 · arxiv updated 2016/05/24

Abstract

We consider the μ-densities spaces F_μ with μ∈ℝ, we compute the space H¹_diff(\mathfrakaff(1),D_λ,μ) where λ=(λ₁,…,λ_n)∈ℝⁿ and D_λ,μ is the space of n-ary differential operators from F_λ1⊗⋯\otimesF_λn to F_μ. We also compute the super analog space H¹_diff(\mathfrakaff(1|1),\mathfrakD_λ,μ).

Citations

• Cohomology of \frak osp(1|2) acting on the space of bilinear differential operators on the superspace ℝ^1|1
• Cohomology of \frak sl(2) acting on the space of n-ary differential operators on ℝ

Related

• Cohomology of \frak sl(2) acting on the space of n-ary differential operators on ℝ
• Second cohomology space of \frak sl(2) acting on the space of n-ary differential operators on ℝ
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• Differential Operators on the Weighted Densities on the Supercircle S^1|n
• The spaces Hⁿ(\mathfrakosp(1|2),M) for some weight modules M