### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 137-150 |

Number of pages | 14 |

Journal | Theoretical and Mathematical Physics |

Volume | 158 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2009 |

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### Keywords

- Conformal structure
- Density tensor
- Invariant operator
- Transvector

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

**Ternary invariant differential operators acting on spaces of weighted densities.** / Bouarroudj, Sofiane.

Research output: Contribution to journal › Article

*Theoretical and Mathematical Physics*, vol. 158, no. 2, pp. 137-150. https://doi.org/10.1007/s11232-009-0012-8

}

TY - JOUR

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

AU - Bouarroudj, Sofiane

PY - 2009/2/1

Y1 - 2009/2/1

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

UR - http://www.scopus.com/inward/record.url?scp=62949181421&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62949181421&partnerID=8YFLogxK

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 -