On the second osp(1|2)-relative cohomology of the lie superalgebra of contact vector fields on C1|1

• Abderraouf Ghallabi ^[1] ; Nizad Ben Fraj ^[1] ; Salem Faidi ^[2]
  1. [1] University of Carthage

     University of Carthage

     Túnez

     
  2. [2] D´epartement de Math´ematiques, Faculé des Sciences de Sfax, Tunisia
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 68, Nº. 2, 2025, págs. 349-367
• Idioma: inglés
• DOI: 10.33044/revuma.3888
• Enlaces
  • Texto completo
• Resumen

  • Let K(1) be the Lie superalgebra of contact vector fields on the (1, 1)-dimensional complex superspace; it contains the M¨obius superalgebra osp(1|2). We classify osp(1|2)-invariant superanti-symmetric binary differential operators from K(1) ∧ K(1) to Dλ,µ vanishing on osp(1|2), where Dλ,µ is the superspace of linear differential operators acting on the superspaces of weighted densities. This result allows us to compute the second differential osp(1|2)-relative cohomology of K(1) with coefficients in Dλ,µ.

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