Abstract
The purpose of the paper is to present a proof of the existence theorem for star-products and formal deformations of the Poisson Lie algebra on a symplectic manifold. The algebraic formalism of formal deformations and the cohomological background needed are described. The method used in the proof of the existence theorem leads to the description of the algebra of derivations of a star-product and, for a non compact manifold, to that of a formal deformation of the Poisson Lie algebra. Graded cohomology is used to classify all 1-differential deformations of the Poisson Lie algebra.
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© 1988 Kluwer Academic Publishers
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De Wilde, M., Lecomte, P. (1988). Formal Deformations of the Poisson Lie Algebra of a Symplectic Manifold and Star-Products. Existence, Equivalence, Derivations. In: Hazewinkel, M., Gerstenhaber, M. (eds) Deformation Theory of Algebras and Structures and Applications. NATO ASI Series, vol 247. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3057-5_18
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DOI: https://doi.org/10.1007/978-94-009-3057-5_18
Publisher Name: Springer, Dordrecht
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