On *-representations of the Hopf *-algebra associated with the quantum group U q (n)
Koelink, H. Tjerk
Compositio Mathematica, Tome 80 (1991), p. 199-231 / Harvested from Numdam
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Publié le : 1991-01-01
@article{CM_1991__77_2_199_0,
     author = {Koelink, H. Tjerk},
     title = {On $\ast $-representations of the Hopf $\ast $-algebra associated with the quantum group $U\_q(n)$},
     journal = {Compositio Mathematica},
     volume = {80},
     year = {1991},
     pages = {199-231},
     mrnumber = {1091898},
     zbl = {0721.17014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1991__77_2_199_0}
}

Koelink, H. Tjerk. On $\ast $-representations of the Hopf $\ast $-algebra associated with the quantum group $U_q(n)$. Compositio Mathematica, Tome 80 (1991) pp. 199-231. http://gdmltest.u-ga.fr/item/CM_1991__77_2_199_0/

1 Bergman, G.M., The diamond lemma for ring theory, Advances Math. 29, 1978, 178-218. | MR 506890 | Zbl 0377.16013

2 Bragiel, K., The twisted SU(3) group. Irreducible *-representations of the C*-algebra C(SμU(C)), Lett. Math. Phys. 17, 1989, 37-44. | Zbl 0706.46054

3 Dixmier, J., Les C*-algèbres et leurs représentations, Gauthier-Villars, 1964. | MR 171173 | Zbl 0152.32902

4 Drinfeld, V.G., Quantum groups, in 'Proc. International Congress of Mathematicians, 1986', American Math. Soc., 1987, 798-820. | MR 934283 | Zbl 0667.16003

5 Faddeev, L.D., N. Yu, Reshetikhin and L.A. Takhtajan, Quantization of Lie groups and Lie algebras, in 'Algebraic Analysis', vol. 1 (eds. M. Kashiwara and T. Kawai), Academic Press, 1988, 129-139. | MR 992450 | Zbl 0677.17010

6 Humphreys, J.E., Introduction to Lie algebras and representation theory, GTM 9, Springer Verlag, 1972. | MR 323842 | Zbl 0254.17004

7 Jimbo, M., A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10, 1985, 63-69. | MR 797001 | Zbl 0587.17004

8 Knapp, A.W., Representation theory of semisimple groups, Princeton University Press, 1986. | MR 855239 | Zbl 0604.22001

9 Koornwinder, T.H., Orthogonal polynomials in connection with quantum groups, in 'Orthogonal Polynomials: Theory and Practice' (ed. P. Nevai), NATO ASI Series C, Vol. 294, Kluwer, 1990, 257-292. | MR 1100297 | Zbl 0697.42019

10 Mackey, G.W., The theory of unitary group representations, The University of Chicago Press, 1976. | MR 396826 | Zbl 0344.22002

11 Manin, Yu. I., Quantum groups and non-commutative geometry, Centre de Recherches Mathématiques, Université de Montreal, 1988. | Zbl 0724.17006

12 Parshall, B. and J.-P. Wang, Quantum linear groups I, preprint, 1989. | MR 1048073

13 Reshetikhin, N. Yu., L.A. Takhtajan and L.D. Faddeev, Quantification of Lie groups and Lie algebras, Algebra i Analiz 1, 1989, 178-206. (In Russian.) | Zbl 0715.17015

14 Rosso, M., An analogue of P. B. W. theorem and the universal R-matrix for Uhsl(N + 1), Comm. Math. Phys. 124, 1989, 307-318. | MR 1012870 | Zbl 0694.17006

15 Rudin, W., Functional analysis, Tata McGraw-Hill, 1974. | Zbl 0253.46001

16 Sakai, S., C*-algebras and W*-algebras, Springer Verlag, 1971. | MR 442701 | Zbl 0219.46042

17 Sweedler, M.E., Hopf algebras, Benjamin, 1969. | MR 252485 | Zbl 0194.32901

18 Takesaki, M., Theory of operator algebras I, Springer Verlag, 1979. | Zbl 0436.46043

19 Vaksman, L.L. and Ya. S. Soibelman, Function algebra on the quantum group SU(2), Funktsional Anal. i. Prilozhen 22 (3), 1988, 1-14,English translation in Functional Anal. Appl. 22(3), 1988, 170-181. | MR 961757 | Zbl 0679.43006

20 Woronowicz, S.L., Twisted SU(2) group. An example of a non-commutative differential calculus, Publ. Res. Inst. Math. Sci. 23, 1987, 117-181. | MR 890482 | Zbl 0676.46050

21 Woronowicz, S.L., Compact matrix pseudogroups, Comm. Math. Phys. 111, 1987, 613-665. | MR 901157 | Zbl 0627.58034

22 Woronowicz, S.L., Tanaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math. 93, 1988, 35-76. | MR 943923 | Zbl 0664.58044

23 Yamane, H., A Poincaré-Birkhoff-Witt theorem for the quantum group of type AN, Proc. Japan Acad. 64, Ser. A, 1988, 385-386. | MR 979952 | Zbl 0677.17011