Letters in Mathematical Physics

, Volume 13, Issue 2, pp 157–166 | Cite as

Application of the cohomology of graded Lie algebras to formal deformations of Lie Algebras

  • P. B. A. Lecomte
Article
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Abstract

The purpose of the Letter is to show how to use the cohomology of the Nijenhuis-Richardson graded Lie algebra of a vector space to construct formal deformations of each Lie algebra structure of that space. One then shows that the de Rham cohomology of a smooth manifold produces a family of cohomology classes of the graded Lie algebra of the space of smooth functions on the manifold. One uses these classes and the general construction above to provide one-differential formal deformations of the Poisson Lie algebra of the Poisson manifolds and to classify all these deformations in the symplectic case.

Keywords

Manifold Statistical Physic Vector Space Smooth Function Group Theory 
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Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • P. B. A. Lecomte
    • 1
  1. 1.Institut de MathematiquesUniversité de LiègeLiègeBelgium

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