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Multiparameter deformations of the universal enveloping algebras of the simple Lie algebras \(A_ l\) for all \(l\geq 2\) and the Yang-Baxter equation. (English) Zbl 0803.17004

Using a known multiparametric quantum \(R\)-matrix, the author takes the approach of Reshetikhin, Takhtadzhyan, and Faddeev, to construct a \(1+{1\over 2} l(l-1)\)-parameter family of quantum analogues of the universal envelope \(U_ q (\text{sl} (l+1, \mathbb{C}))\). The resulting Hopf data have structure similar to those described in [N. Reshetikhin, Lett. Math. Phys. 20, 331-335 (1990; Zbl 0719.17006)] by means of twisting.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
16W30 Hopf algebras (associative rings and algebras) (MSC2000)

Citations:

Zbl 0719.17006
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References:

[1] Reshetikhin N., Alg. Anal. 1 pp 178– (1989)
[2] Takhtajan L., Adv. Stud. Pure Math. 19 pp 435– (1989)
[3] DOI: 10.1007/BF01474085 · doi:10.1007/BF01474085
[4] DOI: 10.1088/0305-4470/24/21/002 · Zbl 0761.17016 · doi:10.1088/0305-4470/24/21/002
[5] DOI: 10.1007/BF02098449 · Zbl 0726.17027 · doi:10.1007/BF02098449
[6] DOI: 10.1142/S0217751X90000027 · Zbl 0709.17009 · doi:10.1142/S0217751X90000027
[7] DOI: 10.1007/BF01555507 · doi:10.1007/BF01555507
[8] DOI: 10.1007/BF00704588 · Zbl 0587.17004 · doi:10.1007/BF00704588
[9] DOI: 10.1007/BF00400222 · Zbl 0602.17005 · doi:10.1007/BF00400222
[10] DOI: 10.1088/0305-4470/23/15/001 · doi:10.1088/0305-4470/23/15/001
[11] DOI: 10.3792/pjaa.66.112 · Zbl 0723.17012 · doi:10.3792/pjaa.66.112
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