Cornwell, J. F. 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 J. Math. Phys. 33, No. 12, 3963-3977 (1992). 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. Reviewer: S.Parmentier (Villeurbanne) 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) Keywords:multiparameter quantum groups; deformation of universal enveloping algebra; simple Lie algebra; quantum Yang-Baxter equation; Hopf algebra Citations:Zbl 0719.17006 PDFBibTeX XMLCite \textit{J. F. Cornwell}, J. Math. Phys. 33, No. 12, 3963--3977 (1992; Zbl 0803.17004) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.