The spaces Hⁿ(\mathfrakosp(1|2),M) for some weight modules M

2009/07/01 by Didier Arnal, Arnal, Didier, Mabrouk Ben Ammar +4
Mathematics · #17B10 #17B56 #17B66 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B10 #msc:17B56 #msc:17B66

paper · pdf · doi:10.48550/arxiv.0907.0224

arxiv created 2009/07/01 · openalex publication_date 2009/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We entirely compute the cohomology for a natural and large class of \mathfrakosp(1|2) modules M. We study the restriction to the \mathfraksl(2) cohomology of M and apply our results to the module M=\mathfrak D_λ,μ of differential operators on the super circle, acting on densities.

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
• Differential Operators on the Weighted Densities on the Supercircle S^1|n
• Symetries of modules of differential operators on S^1|1
• Cohomology of SL₂ and related structures