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Title: Universal enveloping algebras and quantization (English)
Author: Grabowski, Janusz
Language: English
Journal: Proceedings of the Winter School "Geometry and Physics"
Issue: 1991
Pages: [65]-70
Category: math
Summary: 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)]. (English)
MSC: 16S30
MSC: 17B37
MSC: 37J99
MSC: 53D50
MSC: 58F06
MSC: 81S10
idZBL: Zbl 0792.58020
idMR: MR1246621
Date available: 2009-07-13T21:29:01Z
Last updated: 2012-09-18
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