Differential Operators on the Weighted Densities on the Supercircle S^1|n

2013/06/01 by Nader Belghith, Belghith, Nader, Mabrouk Ben Ammar +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #math.DG

paper · pdf · doi:10.48550/arxiv.1306.0101

openalex publication_date 2013/06/01 · arxiv created 2014/04/26 · arxiv updated 2014/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Over the (1,n)-dimensional real supercircle, we consider the K(n)-modules of linear differential operators, \frakDⁿ_λ,μ, acting on the superspaces of weighted densities, where K(n) is the Lie superalgebra of contact vector fields. We give, in contrast to the classical setting, a classification of these modules for n=1. We also prove that \frakDⁿ_λ,μ and \frakD_ρ,νⁿ are isomorphic for ρ=(2-n)/(2)-μ and ν=(2-n)/(2)-λ. This work is the simplest superization of a result by Gargoubi and Ovsienko [Modules of Differential Operators on the Real Line, Functional Analysis and Its Applications, Vol. 35, No. 1, pp. 13--18, 2001.]

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