Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra


Author: George Lusztig
Journal: J. Amer. Math. Soc. 3 (1990), 257-296
MSC: Primary 17B37; Secondary 16W30, 20G40
DOI: https://doi.org/10.1090/S0894-0347-1990-1013053-9
MathSciNet review: 1013053
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [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 $ q$-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)

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 17B37, 16W30, 20G40

Retrieve articles in all journals with MSC: 17B37, 16W30, 20G40


Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1990-1013053-9
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society