Geodesic
Poisson–Lie groups. The quantum duality principle and the twisted quantum double
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 302-329 
M. A. Semenov-Tian-Shansky. Poisson–Lie groups. The quantum duality principle and the twisted quantum double. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 302-329. http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a8/
@article{TMF_1992_93_2_a8,
     author = {M. A. Semenov-Tian-Shansky},
     title = {Poisson{\textendash}Lie groups. {The} quantum duality principle and the twisted quantum double},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {302--329},
     year = {1992},
     volume = {93},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a8/}
}
TY  - JOUR
AU  - M. A. Semenov-Tian-Shansky
TI  - Poisson–Lie groups. The quantum duality principle and the twisted quantum double
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1992
SP  - 302
EP  - 329
VL  - 93
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a8/
LA  - ru
ID  - TMF_1992_93_2_a8
ER  - 
%0 Journal Article
%A M. A. Semenov-Tian-Shansky
%T Poisson–Lie groups. The quantum duality principle and the twisted quantum double
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1992
%P 302-329
%V 93
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a8/
%G ru
%F TMF_1992_93_2_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

The quantum duality principle relates the quantum groups that arise on the quantization of Poisson–Lie dual groups and generalizes Fourier duality. Also considered are the theory of the Heisenberg double, which replaces the cotangent bundle for quantum groups, and its deformations (the twisted double).

[1] Drinfeld V. G., “Quantum Groups”, Proc. of the Internat. Congr. of Math. (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, RI, 1987, 798–820 | MR

[2] Jimbo M., Lett. Math. Phys., 10:1 (1985), 63–69 | DOI | MR | Zbl

[3] Reshetikhin N. Yu., Takhtadzhyan L. A., Faddeev L. D., Algebra i analiz, 1:1 (1989), 178–206 | MR

[4] Faddeev L. D., Reshetikhin N. Yu., Takhtajan L. A., “Quantization of Lie groups and Lie algebras”, Algebraic Analysis, v. 1, eds. Kashiwara M., Kawai T., Academic Press, N. Y., 1988, 129–139 | DOI | MR

[5] Drinfeld B. G., DAN SSSR, 268:5 (1983), 285–287 | MR | Zbl

[6] Weinstein A., J. Diff. Geom., 18 (1983), 523–557 | DOI | MR | Zbl

[7] Berezin F. A., Funkts. analiz i ego prilozh., 1:2 (1967), 1–14 | MR | Zbl

[8] Alekseev A. Yu., Faddeev L. D., Semenov-Tian-Shanski M. A., Hidden quantum group inside Kac-Moody algebra, preprint LOMI E1, LOMI, L., 1991 | MR

[9] Kirillov A. N., Reshetikhin N. Yu., Commun. Math. Phys., 134:2 (1990), 421–431 | DOI | MR | Zbl

[10] Levendorski S., Soibelman Y., J. Geom. Phys., 7:2 (1991), 241–251 | DOI | MR

[11] Rosso M., Commun. Math. Phys., 117 (1988), 307–318 | DOI | MR

[12] Semenov-Tian-Shanski M. A., Publ. RIMS, Kyoto University, 21:6 (1985), 1237–1260 | DOI

[13] Lu J. H., “Momentum mappings and reduction of Poisson actions”, Symplectic geometry, groupoids, and integrable systems, no. 20, eds. P. Dozor, A. Weinstein, MSRI Publications, 1991, 209–226 | MR

[14] Kirillov A. A., Elementy teorii predstavlenii, Nauka, M., 1972 | MR

[15] Reshetikhin N. Yu., Semenov-Tian-Shanski M. A., J. Geom. Phys., 5:4 (1989), 533–550 | DOI | MR

[16] Alekseev A. Yu., Faddeev L. D., Commun. Math. Phys., 141:3 (1991), 413–422 | DOI | MR | Zbl

[17] Reshetikhin N. Yu., Semenov-Tian-Shanski M. A., Lett. Math. Phys., 19:3 (1990), 133–142 | DOI | MR | Zbl

[18] Belavin A. A., Drinfeld V. G., Mathematical physics reviews, v. 4, Soviet Sci. Rev. Sect. C Math. Phys. Rev., 4, Harwood Academic Publ., Chur, 1984, 93–165 | MR

[19] Parmentier S., Twisted Affine Poisson Structures and the Classical Yang-Baxter Equation, preprint MPI/91-82, M. Planck. Institut fur Math., Bonn