Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra

Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra
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J. Amer. Math. Soc. 3 (1990), 257-296

DOI: https://doi.org/10.1090/S0894-0347-1990-1013053-9

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References

Nicolas Bourbaki, Éléments de mathématique, Masson, Paris, 1981 (French). Groupes et algèbres de Lie. Chapitres 4, 5 et 6. [Lie groups and Lie algebras. Chapters 4, 5 and 6]. MR 647314
Claude Chevalley, Certains schémas de groupes semi-simples, Séminaire Bourbaki, Vol. 6, Soc. Math. France, Paris, 1995, pp. Exp. No. 219, 219–234 (French). MR 1611814
Charles W. Curtis, Representations of Lie algebras of classical type with applications to linear groups, J. Math. Mech. 9 (1960), 307–326. MR 0110766, DOI 10.1512/iumj.1960.9.59018
V. G. Drinfel′d, Hopf algebras and the quantum Yang-Baxter equation, Dokl. Akad. Nauk SSSR 283 (1985), no. 5, 1060–1064 (Russian). MR 802128

Hecke algebras and reflections in Coxeter groups

Michio Jimbo, A $q$-difference analogue of $U({\mathfrak {g}})$ and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), no. 1, 63–69. MR 797001, DOI 10.1007/BF00704588
Bertram Kostant, Groups over $Z$, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 90–98. MR 0207713
G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math. 70 (1988), no. 2, 237–249. MR 954661, DOI 10.1016/0001-8708(88)90056-4
G. Lusztig, Modular representations and quantum groups, Classical groups and related topics (Beijing, 1987) Contemp. Math., vol. 82, Amer. Math. Soc., Providence, RI, 1989, pp. 59–77. MR 982278, DOI 10.1090/conm/082/982278

On quantum groups

Marc Rosso, Finite-dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra, Comm. Math. Phys. 117 (1988), no. 4, 581–593. MR 953821, DOI 10.1007/BF01218386
Robert Steinberg, Representations of algebraic groups, Nagoya Math. J. 22 (1963), 33–56. MR 155937, DOI 10.1017/S0027763000011016
Daya-Nand Verma, Structure of certain induced representations of complex semisimple Lie algebras, Bull. Amer. Math. Soc. 74 (1968), 160–166. MR 218417, DOI 10.1090/S0002-9904-1968-11921-4
L. Alvarez-Gaumé, C. Gomez, and G. Sierra, Quantum group interpretation of some conformal field theories, Phys. Lett. B 220 (1989), no. 1-2, 142–152. MR 990842, DOI 10.1016/0370-2693(89)90027-0
Gregory Moore and Nicolai Reshetikhin, A comment on quantum group symmetry in conformal field theory, Nuclear Phys. B 328 (1989), no. 3, 557–574. MR 1030450, DOI 10.1016/0550-3213(89)90219-8