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References

  1. H. H. Andersen, P. Polo and Wen K., Representations of quantum algebras, Inv. Math. (1991).

    Google Scholar 

  2. A. A. Beilinson, R. MacPherson and G. Lusztig, A geometric setting for the quantum deformation of GL, Duke Math. J. 61 (1990).

    Google Scholar 

  3. C. Chevalley, Certains schémas de groupes semisimples,Séminaire Bourbaki (1961/62).

    Google Scholar 

  4. V. G. Drinfeld, Hopf algebras and the Yang-Baxter equation, Soviet Math. Dokl. 32 (1985), 254–258.

    Google Scholar 

  5. M. Dyer and G. Lusztig, Appendix, Geom. Dedicata (1990).

    Google Scholar 

  6. M. Jimbo, A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), 63–69.

    Article  MathSciNet  MATH  Google Scholar 

  7. B. Kostant, Groups over Z Proc. Symp. Pure Math. 9 (1966), 90–98, Amer. Math. Soc.

    Google Scholar 

  8. G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math. 70 (1988), 237–249.

    Article  MathSciNet  MATH  Google Scholar 

  9. G. Lusztig, Modular representations and quantum groups, Contemp. Math. 82 (1989), 59–77, Amer. Math. Soc..

    MathSciNet  Google Scholar 

  10. G. Lusztig, On quantum groups, J. Algebra 131 (1990), 466–475.

    Article  MathSciNet  MATH  Google Scholar 

  11. G. Lusztig, Finite dimensional Hopf algebras arising from quantized universal envelop- ing algebras, Jour. Amer. Math. Soc. 3 (1990), 257–296.

    MathSciNet  MATH  Google Scholar 

  12. G. Lusztig, Quantum groups at roots of 1, Geom. Dedicata (1990).

    Google Scholar 

  13. G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), 447–498;

    Article  MathSciNet  MATH  Google Scholar 

  14. G. Lusztig, Common trends in mathematics and quantum filed theoreis, ed, J. Eguchi et al., Progress of Theor. Physics 102, 175–201.

    Google Scholar 

  15. C. M. Ringel, Hall algebras and quantum groups, Inv. Math.

    Google Scholar 

  16. M. Rosso, Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra, Comm. Math. Phys. 117 (1988), 581–593.

    Article  MathSciNet  MATH  Google Scholar 

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© 1992 Birkhäuser Boston

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Lusztig, G. (1992). Introduction to Quantized Enveloping Algebras. In: Tirao, J., Wallach, N.R. (eds) New Developments in Lie Theory and Their Applications. Progress in Mathematics, vol 105. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2978-0_3

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  • DOI: https://doi.org/10.1007/978-1-4612-2978-0_3

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7743-9

  • Online ISBN: 978-1-4612-2978-0

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