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It is shown how the universal enveloping algebra of a Lie algebra $L$ can be obtained as a formal deformation of the Kirillov-Souriau Poisson algebra $C\sp \infty(L\sp*)$ of smooth functions on the dual of $L$. This deformation process may be viewed as a ``quantization'' in the sense of {\it F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz} and {\it D. Sternheimer} [Ann. Phys. 111, 61-110 (1978; Zbl 0377.53024) and ibid., 111-151 (1978; Zbl 0377.53025)]. The result presented is a somewhat more elaborate version of earlier findings by {\it S. Gutt} [Lett. Math. Phys. 7, 249-258 (1983; Zbl 0522.58019)] and {\it V. G. Drinfel'd} [Sov. Math., Dokl. 28, 667-671 (1983); translation from Dokl. Akad. Nauk SSSR 273, No. 3, 531-535 (1983; Zbl 0553.58038)].
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