Geodesic
Notes on the differential calculi on quantum linear groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 148-152 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This talk is devoted to the problem of construction of the differential calculi on quantum linear groups. Basing on the natural algebraic postulates we examine the possible commutation relations for the $GL_q(N)$- and $SL_q(N)$-invariant differential forms and vector fields. It turns out that there exist several families of the admissible commutation rules for $GL_q(N)$, but, in contrast, the commutation prescription for $SL_q(N)$ is unique. 
@article{TMF_1994_100_1_a13,
     author = {P. N. Pyatov and P. A. Saponov},
     title = {Notes on the differential calculi on quantum linear groups},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {148--152},
     year = {1994},
     volume = {100},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a13/}
}
TY  - JOUR
AU  - P. N. Pyatov
AU  - P. A. Saponov
TI  - Notes on the differential calculi on quantum linear groups
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 148
EP  - 152
VL  - 100
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a13/
LA  - ru
ID  - TMF_1994_100_1_a13
ER  - 
%0 Journal Article
%A P. N. Pyatov
%A P. A. Saponov
%T Notes on the differential calculi on quantum linear groups
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 148-152
%V 100
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a13/
%G ru
%F TMF_1994_100_1_a13
P. N. Pyatov; P. A. Saponov. Notes on the differential calculi on quantum linear groups. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 148-152. http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a13/

[1] S. L. Woronowicz, Comm. Math. Phys., 122 (1989), 125 | DOI | MR | Zbl

[2] L. D. Faddeev, N. Reshetikhin, L. Takhtajan, Alg. i Anal., 1 (1989), 178 | MR

[3] G. Maltsiniotis, C. R. Acad. Sci. Paris, 331 (1990), 831–834 | MR

[4] A. Sudbery, Phys. Lett. B, 284 (1992), 61 | DOI | MR

[5] A. Schirrmacher, Groups and Related Topics, eds. R. Gielerak et al., Kluwer Academic Publishers, 1992, 55 | DOI | MR | Zbl

[6] P. Schupp, P. Watts, B. Zumino, Lett. Math. Phys., 25 (1992), 139 | DOI | MR | Zbl

[7] A. P. Isaev, P. N. Pyatov, Phys. Lett. A, 179 (1993), 81 ; A. P. Isaev, P. N. Pyatov, Covariant Differential Complexes on Quantum Linear Groups, JINR preprint E2-93-416 ; J. Phys. A, 28:8 (1995), 2227–2246 | DOI | MR | MR | DOI | Zbl

[8] M. Jimbo, Lett. Math. Phys., 10 (1985), 63 ; 11 (1986), 247 | DOI | MR | Zbl | DOI | MR | Zbl

[9] N. Yu. Reshetikhin, Alg. i Anal., 1:2 (1989), 169 | MR

[10] H. Weyl, Theory of Groups and Quantum Mechanics, Dover Publications, Inc., 1931 | MR

[11] G. Lusztig, Adv. in Math., 70 (1988), 237 ; M. Rosso, C. R. Acad. Sci. Paris{, ser. I}, 305 (1987), 587 | DOI | MR | Zbl | MR | Zbl

[12] Yu. Manin, Comm. Math. Phys., 122 (1989), 163 | DOI | MR