On the Cohomology of the spaces of differential operators acting on skewsymmetric tensor fields or on forms, as modules of the Lie algebra of vector fields

2002/08/30 by Boujemaâ Agrebaoui, B. Agrebaoui, F. Ammar +6
Mathematics · #17B66 #58A99 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:17B66 #msc:58A99

paper · pdf · doi:10.48550/arxiv.math/0208251

12 pages

arxiv created 2002/08/30 · openalex publication_date 2002/08/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The space of differential operators acting on skewsymmetric tensor fields or on smooth forms of a smooth manifold are representations of its Lie algebra of vector fields. We compute the first cohomology spaces of these representations and show how they are related to the cohomology with coefficients in ther space of smooth functions of the manifold.

Related

• Cohomology of the vector fields Lie algebra and modules of differential operators on a smooth manifold
• Space of second order linear differential operators as a module over the Lie algebra of vector fields
• Symmetry via Lie algebra cohomology
• Projectively invariant symbol map and cohomology of vector fields Lie algebras intervening in quantization
• Multi-parameter deformations of the module of symbols of differential operators