### 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) |
---|---|

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 |

### Keywords

- Conformal structure
- Density tensor
- Invariant operator
- Transvector

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics