Ternary invariant differential operators acting on spaces of weighted densities

Sofiane Bouarroudj

    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

    Fingerprint

    Invariant Differential Operators
    differential operators
    Ternary
    operators
    Operator
    Invariant
    Vector Field
    Lie Algebra
    algebra
    Dualization
    Invariant Operator
    Poisson Bracket
    Antisymmetric
    permutations
    Exception
    brackets
    Differential operator
    n-dimensional
    lists
    Permutation

    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.

    In: Theoretical and Mathematical Physics, Vol. 158, No. 2, 01.02.2009, p. 137-150.

    Research output: Contribution to journalArticle

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