Universal enveloping algebras and quantization

Grabowski, Janusz. "Universal enveloping algebras and quantization." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1993. [65]-70. <http://eudml.org/doc/220653>.

@inProceedings{Grabowski1993,
abstract = {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 $C^\infty (L^*)$ of smooth functions on the dual of $L$. This deformation process may be viewed as a “quantization” in the sense of F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and 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 S. Gutt [Lett. Math. Phys. 7, 249-258 (1983; Zbl 0522.58019)] and 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)].},
author = {Grabowski, Janusz},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Proceedings; Geometry; Srní (Czechoslovakia); Physics},
location = {Palermo},
pages = {[65]-70},
publisher = {Circolo Matematico di Palermo},
title = {Universal enveloping algebras and quantization},
url = {http://eudml.org/doc/220653},
year = {1993},
}

TY - CLSWK
AU - Grabowski, Janusz
TI - Universal enveloping algebras and quantization
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1993
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [65]
EP - 70
AB - 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 $C^\infty (L^*)$ of smooth functions on the dual of $L$. This deformation process may be viewed as a “quantization” in the sense of F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and 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 S. Gutt [Lett. Math. Phys. 7, 249-258 (1983; Zbl 0522.58019)] and 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)].
KW - Proceedings; Geometry; Srní (Czechoslovakia); Physics
UR - http://eudml.org/doc/220653
ER -