Ternary invariant differential operators acting on spaces of weighted
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 165-180
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We classify ternary differential operators over $n$-dimensional manifolds. These operators act on the spaces of weighted densities and are 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 antisymmetric operators; four of the operators are new up to dualizations and permutations. For $n>1$, we list multidimensional conformal tranvectors, i.e., operators acting on the spaces of weighted densities and invariant with respect to $\mathfrak o(p+1,q+1)$, where $p+q=n$. With
the exception of the scalar operator, these conformally invariant operators are not invariant with respect to the whole Lie algebra of vector fields.
Keywords:
invariant operator, density tensor
Mots-clés : transvector, conformal structure.
Mots-clés : transvector, conformal structure.
@article{TMF_2009_158_2_a0,
author = {S. Bouarroudj},
title = {Ternary invariant differential operators acting on spaces of weighted},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {165--180},
publisher = {mathdoc},
volume = {158},
number = {2},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a0/}
}
S. Bouarroudj. Ternary invariant differential operators acting on spaces of weighted. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 165-180. http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a0/