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ISSN 1088-6834(e) ISSN 0894-0347(p)

Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra

Author(s): George Lusztig
Journal: J. Amer. Math. Soc. 3 (1990), 257-296.
MSC: Primary 17B37; Secondary 16W30, 20G40
MathSciNet review: 1013053
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References:

[1]: N. Bourbaki, Groupes et algèbres de Lie, Chapitres 4, 5, et 6, Masson, Paris, 1981. MR 647314 (83g:17001)
[2]: C. Chevalley, Certains schémas de groupes semi-simples, Sém. Bourbaki 1960/61, no 219. MR 1611814
[3]: C. W. Curtis, Representations of Lie algebras of classical type with applications to linear gorups, J. Math. Mech. 9 (1960), 307-326. MR 0110766 (22:1634)
[4]: V. G. Drinfel'd, Hopf algebras and the quantum Yang-Baxter equation, Soviet Math. Dokl. 32 (1985), 254-258. MR 802128 (87h:58080)
[5]: M. Dyer, Hecke algebras and reflections in Coxeter groups, Ph. D. thesis, University of Sydney, 1987.
[6]: M. Jimbo, A -difference analogue of $U(\mathfrak{g})$ and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), 63-69. MR 797001 (86k:17008)
[7]: B. Kostant, Groups over $\mathbb{Z}$ , Proc. Sympos. Pure Math., Vol. 9, Amer. Math. Soc., Providence, R. I., 1966, pp. 90-98. MR 0207713 (34:7528)
[8]: G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math. 70 (1988), 237-249. MR 954661 (89k:17029)
[9]: -, Modular representations and quantum groups, Contemp. Math., Vol. 82, Amer. Math. Soc., Providence, R. I., 1989, pp. 59-77. MR 982278 (90a:16008)
[10]: -, On quantum groups, J. Algebra (to appear).
[11]: M. Rosso, Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simplex Lie algebra, Comm. Math. Phys. 117 (1988), 581-593. MR 953821 (90c:17019)
[12]: R. Steinberg, Representations of algebraic groups, Nagoya Math. J. 22 (1963), 33-56. MR 0155937 (27:5870)
[13]: D. N. Verma, Structure of certain induced representations of complex semisimple Lie algebras, Bull. Amer. Math. Soc. 74 (1968), 160-168. MR 0218417 (36:1503)
[14]: L. Alvarez-Gaumé, C. Gomez, and G. Sierra, Quantum group interpretation of some conformal filed theories, preprint CERN-TH-5267/88, Cern, Geneva, 1988. MR 990842 (90f:17015)
[15]: G. Moore and N. Reshetikhin, A comment on quantum group symmetry in conformal field theory, preprint IASSNS-HEP-89, Inst. for Adv. Study, Princeton, N. J., 1989. MR 1030450 (91c:81145)

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