The q-bracket product and quantum enveloping algebras of classical types

Mitsuhiro TAKEUCHI

doi:10.2969/jmsj/04240605

Mitsuhiro TAKEUCHI

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JOURNAL FREE ACCESS

1990 Volume 42 Issue 4 Pages 605-629

DOI https://doi.org/10.2969/jmsj/04240605

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Published: 1990 Received: September 21, 1989 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) G. M. Bergman, The diamond lemma for ring theory, Adv. in Math., 29 (1978), 178-218.
2) V. G. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation, Soviet Math. Dokl., 32 (1985), 254-258.
3) V. G. Drinfeld, Quantum groups, Proc. ICM, Berkeley 1986, pp. 798-820.
4) M. Jimbo, A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys., 10 (1985), 63-69.
5) V. G. Kac, Infinite dimensional Lie algebras, Progr. Math., 44, Birkhäuser, Boston-Basel-Stuttgart, 1983.
6) G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math., 70 (1988), 237-249.
7) M. Rosso, An analogue of PBW theorem and the universal R-matrix for U_h^sl(N+1), Comm. Math. Phys., 124 (1989), 307-318.
8) T. Tanisaki, Harish-Chandra isomorphisms for quantum algebras, preprint.
9) H. Yamane, A Poincaré-Birkhoff-Witt theorem for quantized universal enveloping algebras of type A_N, Publ. Res. Inst. Math. Sci. Kyoto Univ., 25 (1989), 503-520.
10) G. Lusztig, Finite dimensional Hopf algebras arising from quantum groups, J. Amer. Math. Soc., 3(1990), 257-296.
11) G. Lusztig, Quantum groups at roots of 1, preprint.

Right : [1] G. M. Bergman, The diamond lemma for ring theory, Adv. in Math., 29 (1978), 178-218.
[2] V. G. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation, Soviet Math. Dokl., 32 (1985), 254-258.
[3] V. G. Drinfeld, Quantum groups, Proc. ICM, Berkeley 1986, pp. 798-820.
[4] M. Jimbo, A q-difference analogue of U (g) and the Yang-Baxter equation, Lett. Math. Phys., 10 (1985), 63-69.
[5] V. G. Kac, Infinite dimensional Lie algebras, Progr. Math., 44, Birkhäuser, Boston-Basel-Stuttgart, 1983.
[6] G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math., 70 (1988), 237-249.
[7] M. Rosso, An analogue of PBW theorem and the universal R-matrix for U_hsl (N+1), Comm. Math. Phys., 124 (1989), 307-318.
[8] T. Tanisaki, Harish-Chandra isomorphisms for quantum algebras, preprint.
[9] H. Yamane, A Poincaré-Birkhoff-Witt theorem for quantized universal enveloping algebras of type A_N, Publ. Res. Inst. Math. Sci. Kyoto Univ., 25 (1989), 503-520.
[10] G. Lusztig, Finite dimensional Hopf algebras arising from quantum groups, J. Amer. Math. Soc., 3 (1990), 257-296.
[11] G. Lusztig, Quantum groups at roots of 1, preprint.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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