Geodesic
Quantum groups, $q$ oscillators, and covariant algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 2, pp. 193-199 
P. P. Kulish. Quantum groups, $q$ oscillators, and covariant algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 2, pp. 193-199. http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a1/
@article{TMF_1993_94_2_a1,
     author = {P. P. Kulish},
     title = {Quantum groups, $q$ oscillators, and covariant algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {193--199},
     year = {1993},
     volume = {94},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a1/}
}
TY  - JOUR
AU  - P. P. Kulish
TI  - Quantum groups, $q$ oscillators, and covariant algebras
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1993
SP  - 193
EP  - 199
VL  - 94
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a1/
LA  - ru
ID  - TMF_1993_94_2_a1
ER  - 
%0 Journal Article
%A P. P. Kulish
%T Quantum groups, $q$ oscillators, and covariant algebras
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1993
%P 193-199
%V 94
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a1/
%G ru
%F TMF_1993_94_2_a1

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

The physical interpretation of the basic concepts of the theory of covariant groups–coproducts, representations and corepresentations, action and coaction–is discussed for the examples of the simplest $q$ deformed objects (quantum groups and algebras, $q$ oscillators, and comodule algebras). It is shown that the reduction of the covariant algebra of quantum second-rank tensors includes the algebras of theq oscillator and quantum sphere. A special case of covariant algebra corresponds to the braid group in a space with nontrivial topology.

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

[2] Moore G., Reshetikhin N., Nucl. Phys., B328 (1989), 557 ; Решетихин Н. Ю., Семенов-Тянь-Шанский М. А., Letters in Math. Phys., 19 (1990), 133 | DOI | MR | DOI | MR | Zbl

[3] Alvarez-Gaumé L., Gómez C., Sierra G., Nucl. Phys., B330 (1990), 347 | DOI | MR | Zbl

[4] Pasqnier V., Saleur H., Nucl. Phys., B330 (1990), 523 | DOI

[5] Kulish P., Sklyanin E., J. Phys., A24 (1991), L435 | MR | Zbl

[6] Kulish P., Quantum groups and quantum algebras as symmetries of dynamical systems, preprint YITP/K-959, Kyoto, 1991 | MR

[7] Zumino B., Introduction to differential geometry of quantum groups, preprint UCBPTH-62/91, Berkeley, 1991 | MR

[8] Carrow-Watamura U. et al, Z. Phys., S48 (1990), 159 | MR

[9] Kulish P. P. (ed.), Quantum groups, Proc. Euler Intern. Math. Inst., Lect. Notes in Math., 1510, Springer, Berlin, 1992, 398 pp. | DOI | MR | Zbl

[10] Kulish P. P., Sklyanin E., Algebraic structures related to reflection equations, preprint YITP/K-980, Kyoto, 1992 | MR

[11] Drinfel{\cprime}d V. G., “Quantum groups”, Proc. ICM-86, V. 1, Berkeley, 1987, 798 | MR | Zbl

[12] Takhtajan L. A., “Quantum groups”, Lect. Notes in Physics, 370, Springer, Berlin, 1990, 3 | DOI | MR

[13] Kulish P. P., TMF, 86 (1991), 157 | MR | Zbl

[14] Majid S., Intern. Journ. Mod. Phys., A5 (1990), 1 ; J. Math. Phys., 32 (1991), 3246 | DOI | MR | DOI | MR | Zbl

[15] Faddeev L. D., Takhtajan L. A., “Quantum groups”, Lect. Notes in Phys., 246, 1986, 166 | DOI | MR

[16] Manin Yu., Topics in noncommutative geometry, preprint, Princeton, 1991 | MR

[17] Sossinsky A., Lect. Notes in Math., 1510, 1992, 354 | DOI | MR

[18] Podles̀ P., Lett. Math. Phys., 14 (1987), 193 ; Noumi M., Mimachi K., Comm. Math. Phys., 128 (1990), 521 | DOI | MR | Zbl | DOI | MR | Zbl

[19] Podles̀ P., Quantization enforces interaction, preprint RIMS-817, 1991