arXiv 0806.10442008-06-05math.RTmath-phmath.MP

The ternary invariant differential operators acting on the spaces of weighted densities

Sofiane Bouarroudj

备注：: 13 pages, no figures, to appear in Theor. Math. Phys
发表信息：: Theor. Math. Phys., 158, no. 2, (2009), 137-150.
DOI：: 10.1007/s11232-009-0012-8

英文摘要：

Over n-dimensional manifolds, I classify ternary differential operators acting on the spaces of weighted densities and invariant with respect to the Lie algebra of vector fields. For n=1, some of these operators can be expressed in terms of the de Rham exterior differential, the Poisson bracket, the Grozman operator and the Feigin-Fuchs anti-symmetric operators; four of the operators are new, up to dualizations and permutations. For n>1, I list multidimensional conformal tranvectors, i.e.,operators acting on the spaces of weighted densities and invariant with respect to o(p+1,q+1), where p+q=n. Except for the scalar operator, these conformally invariant operators are not invariant with respect to the whole Lie algebra of vector fields.

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