TY - JOUR

T1 - Ternary invariant differential operators acting on spaces of weighted densities

AU - Bouarroudj, S.

N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2009/2

Y1 - 2009/2

N2 - 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 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.

AB - 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 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.

KW - Conformal structure

KW - Density tensor

KW - Invariant operator

KW - Transvector

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U2 - 10.1007/s11232-009-0012-8

DO - 10.1007/s11232-009-0012-8

M3 - Article

AN - SCOPUS:62949181421

VL - 158

SP - 137

EP - 150

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

IS - 2

ER -