Multi-Derivations and Kähler Forms

  • Camille Laurent-Gengoux
  • Anne Pichereau
  • Pol Vanhaecke
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 347)

Abstract

The algebraic structure of the space of differential forms on a manifold is well-known; the algebraic structure on the space of multi-vector fields may be less well-known. We present both here, together with the algebraic counterpart of these spaces, which are respectively the spaces of Kähler forms and of skew-symmetric multi-derivations of an algebra. It leads to the Gerstenhaber structure on the space of multi-vector fields of a given manifold (or multi-derivations of a given algebra), a space in which the Poisson structure lives and which acts on the space of differential forms on the manifold (Kähler forms of the algebra), via the generalized Lie derivative.

Keywords

Differential Form Poisson Bracket Poisson Structure Wedge Product Grade Vector Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Camille Laurent-Gengoux
    • 1
  • Anne Pichereau
    • 2
  • Pol Vanhaecke
    • 3
  1. 1.CNRS UMR 7122, Laboratoire de MathématiquesUniversité de LorraineMetzFrance
  2. 2.CNRS UMR 5208, Institut Camille JordanUniversité Jean MonnetSaint-EtienneFrance
  3. 3.CNRS UMR 7348, Lab. Mathématiques et ApplicationsUniversité de PoitiersFuturoscope ChasseneuilFrance

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