Ternary invariant differential operators acting on spaces of weighted densities

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)137-150
Number of pages14
JournalTheoretical and Mathematical Physics
Volume158
Issue number2
DOIs
StatePublished - Feb 1 2009

Keywords

  • Conformal structure
  • Density tensor
  • Invariant operator
  • Transvector

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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