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Quantization of Lie group and algebra of \(G_ 2\) type in the Faddeev-Reshetikhin-Takhtajan approach. (English) Zbl 0856.17016

Summary: Based on the quantized universal enveloping (QUE) algebras, a quantization of the automorphism group of some nonassociative algebras is given in the formulation employing noncommuting matrix entries. A quantum group of \(G_2\) type included in this scheme is studied in detail in the Faddeev-Reshetikhin-Takhtajan approach. Also in the formulation employing noncommuting matrix entries, the QUE-algebra of \(G_2\) type is reconstructed through the pairing induced by the \(R\)-matrix between the quantum group and the QUE-algebra.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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References:

[1] Drinfel’d V. G., Proc. Internat. Congr. Math. pp 798– (1986)
[2] DOI: 10.1007/BF00704588 · Zbl 0587.17004 · doi:10.1007/BF00704588
[3] Yu. Reshetikhin N., Leningrad Math. J. 1 pp 193– (1990)
[4] DOI: 10.1007/BF01219077 · Zbl 0627.58034 · doi:10.1007/BF01219077
[5] DOI: 10.1007/BF01219077 · Zbl 0627.58034 · doi:10.1007/BF01219077
[6] DOI: 10.1007/BF00402893 · Zbl 0760.17009 · doi:10.1007/BF00402893
[7] DOI: 10.1007/BF01221411 · Zbl 0751.58042 · doi:10.1007/BF01221411
[8] DOI: 10.1215/S0012-7094-90-06102-2 · Zbl 0721.17013 · doi:10.1215/S0012-7094-90-06102-2
[9] DOI: 10.1007/BF00403543 · Zbl 0753.17020 · doi:10.1007/BF00403543
[10] DOI: 10.1007/BF01218386 · Zbl 0651.17008 · doi:10.1007/BF01218386
[11] DOI: 10.1016/0001-8708(88)90056-4 · Zbl 0651.17007 · doi:10.1016/0001-8708(88)90056-4
[12] DOI: 10.1142/S0217751X90000027 · Zbl 0709.17009 · doi:10.1142/S0217751X90000027
[13] DOI: 10.1142/S0217751X92002805 · Zbl 0972.17501 · doi:10.1142/S0217751X92002805
[14] Okubo S., Alg. Group. Geom. 3 pp 60– (1986)
[15] DOI: 10.1007/BF02096556 · Zbl 0721.17016 · doi:10.1007/BF02096556
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