4 research outputs found
The linear \protect \mathfrak{n}(1|N)–invariant differential operators and \protect \mathfrak{n}(1|N)–relative cohomology
Over the -dimensional supercircle , we classify -invariant linear differential operators acting on the superspaces of weighted densities on , where is the Heisenberg Lie superalgebra. This result allows us to compute the first differential -relative cohomology of the Lie superalgebra of contact vector fields with coefficients in the superspace of weighted densities. For we investigate the first -relative cohomology space associated with the embedding of in the superspace of the supercommutative algebra of pseudodifferential symbols on and in the Lie superalgebra of superpseudodifferential operators with smooth coeffcients. We explicity give 1-cocycles spanning these cohomology spaces
The linear \protect \mathfrak{n}(1|N)–invariant differential operators and \protect \mathfrak{n}(1|N)–relative cohomology
Over the -dimensional supercircle , we classify -invariant linear differential operators acting on the superspaces of weighted densities on , where is the Heisenberg Lie superalgebra. This result allows us to compute the first differential -relative cohomology of the Lie superalgebra of contact vector fields with coefficients in the superspace of weighted densities. For we investigate the first -relative cohomology space associated with the embedding of in the superspace of the supercommutative algebra of pseudodifferential symbols on and in the Lie superalgebra of superpseudodifferential operators with smooth coeffcients. We explicity give 1-cocycles spanning these cohomology spaces