Abstract
Following the ideas presented in q-alg/9709040, we give the definition of Kontsevich star products for linear Poisson structures on ℝd. We prove that all these structures are equivalent and can be defined by integral formulae. Finally, we characterize, among these star products, the Gutt and Duflo star products.
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Kontsevich, M.: Deformation quantization on Poisson manifolds. I, Preprint, q-alg./9709040 (1997).
Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A. and Sternheimer, D.: Deformation theory and quantization I. Deformation of symplectic structures, Ann. Phys. 111(1) (1978), 61–110.
Gutt, S.: An explicit ⋆ product on the cotangent bundle of a Lie group, Lett. Math. Phys. 7(3) (1983), 249–259.
Duflo, M.: Caractères des algèbres de Lie résolubles, CR Acad. Sci. A 269 (1969), 437–438.
Arnal, D.: Le produit star de Kontsevich sur le dual d'une algèbre de Lie nilpotente, To appear in CR Acad. Sci. 327 (1998), 823–826.
Magnus, W., Karrass, A. and Solitar, D.: Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, Dover, New York, 1976.
Varadarajan, V. S.: Lie Groups, Lie Algebras and their Representations, Springer-Verlag, Berlin, 1984.
Duflo, M.: Private communication.
Dito, G.: Kontsevich star-product on the dual of a Lie algebra, Lett. Math. Phys. 48 (1999), 307–322 (this issue).
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Arnal, D., Amar, N.B. & Masmoudi, M. Cohomology of Good Graphs and Kontsevich Linear State Products. Letters in Mathematical Physics 48, 291–306 (1999). https://doi.org/10.1023/A:1007618914771
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DOI: https://doi.org/10.1023/A:1007618914771