Quantum groups, $q$ oscillators, and covariant algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 2, pp. 193-199 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
@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
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/

[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