[Le principe de dualité quantique]
Le “principe de dualité quantique” affirme que la quantification d’une bigèbre de Lie -
moyennant une algèbre enveloppante universelle quantifiée (en abrégé, une QUEA) - donne
aussi une quantification de la bigèbre de Lie duale (via son groupe de Poisson formel
associé) - moyennant une algèbre de Hopf de séries formelles (QFSHA) - et, vice versa,
une QFSHA associée à une bigèbre de Lie (via son groupe de Poisson formel associé) donne
également une QUEA pour la bigèbre de Lie duale. Plus précisément, il existe deux
foncteurs
The “quantum duality principle” states that the quantization of a Lie bialgebra – via a
quantum universal enveloping algebra (in short, QUEA) – also provides a quantization of
the dual Lie bialgebra (through its associated formal Poisson group) – via a quantum
formal series Hopf algebra (QFSHA) — and, conversely, a QFSHA associated to a Lie
bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie
bialgebra as well; more in detail, there exist functors
Keywords: quantum groups, topological Hopf algebras
Mots-clés : groupes quantiques, algèbres de Hopf topologiques
Gavarini, Fabio 1
@article{AIF_2002__52_3_809_0, author = {Gavarini, Fabio}, title = {The quantum duality principle}, journal = {Annales de l'Institut Fourier}, pages = {809--834}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {52}, number = {3}, year = {2002}, doi = {10.5802/aif.1902}, zbl = {1054.17011}, mrnumber = {1907388}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1902/} }
TY - JOUR AU - Gavarini, Fabio TI - The quantum duality principle JO - Annales de l'Institut Fourier PY - 2002 SP - 809 EP - 834 VL - 52 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1902/ DO - 10.5802/aif.1902 LA - en ID - AIF_2002__52_3_809_0 ER -
Gavarini, Fabio. The quantum duality principle. Annales de l'Institut Fourier, Tome 52 (2002) no. 3, pp. 809-834. doi : 10.5802/aif.1902. https://aif.centre-mersenne.org/articles/10.5802/aif.1902/
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