Geodesic
Quantum groups: from Kulish–Reshetikhin discovery to classification
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 186-195 Cet article a éte moissonné depuis la source Math-Net.Ru

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The aim of this paper is to provide an overview of the results about classification of quantum groups that were obtained in [10,11]. 
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B. Kadets; E. Karolinsky; I. Pop; A. Stolin. Quantum groups: from Kulish–Reshetikhin discovery to classification. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 186-195. http://geodesic.mathdoc.fr/item/ZNSL_2015_433_a8/

[1] A. Belavin, V. Drinfeld, “Triangle equations and simple Lie algebras”, Soviet Sci. Rev. Sect. C. Math. Phys. Rev., 4 (1984), 93–165 | MR | Zbl

[2] V. Coll, M. Gerstenhaber, A. Giaquinto, “Ann explicit deformation formula with non-commuting derivations”, Israel Math. Conf. Proceedings, 1 (1989), 396–403 | MR | Zbl

[3] V. Drinfel'd, “Hopf algebras and the quantum Yang–Baxter equation”, Dokl. Akad. Nauk SSSR, 283:5 (1985), 1060–1064 | MR | Zbl

[4] V. Drinfel'd, “Constant quasiclassical solitons of the Yang–Baxter quantum equation”, Soviet Math. Doklady, 28 (1983), 667–671 | MR | Zbl

[5] P. Etingof, D. Kazhdan, “Quantization of Lie bialgebras. I”, Sel. Math. (NS), 2 (1996), 1–41 | DOI | MR | Zbl

[6] P. Etingof, D. Kazhdan, “Quantization of Lie bialgebras. II”, Sel. Math. (NS), 4 (1998), 213–232 | DOI | MR

[7] P. Etingof, T. Schedler, O. Schiffmann, “Explicit quantization of dynamical $r$-matrices for finite dimensional semisimple Lie algebras”, J. Amer. Math. Soc., 13:3 (2000), 595–609 | DOI | MR | Zbl

[8] P. Etingof, O. Schiffmann, Lectures on Quantum Groups, International Press, Cambridge, 1988 | MR

[9] M. Jimbo, “A $q$-difference analogue of $U\mathfrak g$ and the Yang–Baxter equation”, Lett. Math. Phys., 10 (1985), 63–69 | DOI | MR | Zbl

[10] B. Kadets, E. Karolinsky, I. Pop, A. Stolin, Classification of quantum groups and Belavin–Drinfeld cohomologies, 28 pp., arXiv: 1303.4046[math.QA]

[11] B. Kadets, E. Karolinsky, I. Pop, A. Stolin, Classification of quantum groups and Belavin–Drinfeld cohomologies for orthogonal and symplectic Lie algebras, 17 pp., arXiv: 1502.00403[math.QA]

[12] P. P. Kulish, A. I. Mudrov, “Universal $R$-matrix for esoteric quantum groups”, Lett. Math. Phys., 47:2 (1999), 139–148 | DOI | MR | Zbl

[13] P. P. Kulish, N. Yu. Reshetikhin, “Quantum linear problem for the sine-Gordon equation and higher representations”, J. Sov. Math., 23 (1983), 2435–2441 | DOI | MR

[14] P. P. Kulish, A. A. Stolin, “Deformed Yangians and integrable models”, Czechoslovak J. Phys., 47:12 (1997), 1207–1212, Presented at 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrables Systems” (Prague, 19–21 June 1997) | DOI | MR | Zbl

[15] F. Montaner, A. Stolin, E. Zelmanov, “Classification of Lie bialgebras over current algebras”, Selecta Math. (N.S.), 16:4 (2010), 935–962 | DOI | MR | Zbl

[16] I. Pop, A. Stolin, Classification of quantum groups and Lie bialgebra structures on $sl(n,F)$. Relations with Brauer group, 17 pp., arXiv: 1402.3083[math.QA]

[17] A. Stolin, “Some remarks on Lie bialgebra structures on simple complex Lie algebras”, Comm. Algebra, 27:9 (1999), 4289–4302 | DOI | MR | Zbl