Projective and conformal Schwarzian derivatives and cohomology of Lie algebras vector fields related to differential operators

Sofiane Bouarroudj

    Research output: Contribution to journalArticle

    Abstract

    Let M be either a projective manifold (M, Π) or a pseudo-Riemannian manifold (M, g). We extend, intrinsically, the projective/conformal Schwarzian derivatives we have introduced recently, to the space of differential operators acting on symmetric contravariant tensor fields of any degree on M. As operators, we show that the projective/conformal Schwarzian derivatives depend only on the projective connection Π and the conformal class of the metric [g], respectively. Furthermore, we compute the first cohomology group of Vect (M) with coefficients in the space of symmetric contravariant tensor fields valued in the space of δ-densities, and we compute the corresponding sl (n + 1, ℝ)-relative cohomology group.

    Original languageEnglish (US)
    Pages (from-to)667-696
    Number of pages30
    JournalInternational Journal of Geometric Methods in Modern Physics
    Volume3
    Issue number4
    DOIs
    StatePublished - Jun 1 2006

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    differential operators
    homology
    algebra
    tensors
    operators
    coefficients

    Keywords

    • Gelfand-Fuchs cohomology
    • Invariant operators
    • Projective/conformal structures
    • The Schwarzian derivative

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

    Cite this

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