Abstract
The universal quantumR-matrix is obtained in the case of the affine Kac-Moody Lie algebra sl(2).
Similar content being viewed by others
References
Drinfeld, V., Quantum groups,Proc. Internat. Congr. Math., Berkeley, Vol. 1, 1988, pp. 798–820.
Rosso, M., An analogue of PBW theorem and the universalR-matrix for U h (sl(N + 1)),Comm. Math. Phys. 124, 307–318 (1989).
Levendorskii, S. and Soibelman, Ya., Some applications of quantum Weyl group,J. Geom. Phys. 7(2), 1–14 (1990).
Soibelman, Ya., Algebra of functions on compact quantum group and its representations,Algebra i Analiz 2(1), 190–212 (1990) (translated inLeningrad Math. J.).
Soibelman, Ya. and Vaksman, L., Algebra of functions on quantum group SU(2),Funktsional. Anal. i Prilozhen. 22(3), 1–14 (1988).
Soibelman, Ya., Gelfand-Naimark-Segal states and then Weyl group for the quantum group SU(n),Funktsional. Anal. i Prilozhen. 24(3) (1990).
Lusztig, G., Quantum groups at root of 1,Geom. Dedicata 35, 89–114 (1990).
Kirillov, A. and Reshetikhin, N.,q-Weyl groups andR-matrices,Comm. Math. Phys. 134, 421–431 (1990).
Levendorskii, S. and Soibelman, Ya., Algebras of functions on compact quantum groups, Schubert cells and quantum tori,Comm. Math. Phys. 139, 141–170 (1991).
Soibelman, Ya., Selected topics in quantum groups, Preprint RIMS, Kyoto Univ. N 804, andInfinite Analysis, Vol. 2, World Scientific, Singapore.
Belavin, A. and Drinfeld, V., Triangles equations and simple Lie algebras, Preprint of the Inst. Theor. Phys. im. Landau, 1982-18 (1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Levendorskii, S., Soibelman, Y. & Stukopin, V. The quantum Weyl group and the universal quantumR-matrix for affine lie algebraA (1)1 . Lett Math Phys 27, 253–264 (1993). https://doi.org/10.1007/BF00777372
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00777372