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Yang-Baxter deformations of complex simple Lie algebras. (English) Zbl 0906.17012
Slovák, Jan (ed.), Proceedings of the 15th Winter School on geometry and physics, Srní, Czech Republic, January 14–21, 1995. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43, 189-197 (1996).
Summary: It is possible, given any solution of the constant Yang-Baxter equation, to construct an algebra by replacing the standard relators of complex simple Lie algebras by their braided analogs. In particular the one-parameter deformations $$U_q(g)$$ of Drinfeld and Jimbo arise as images of the Yang-Baxter algebras.
For the entire collection see [Zbl 0884.00042].
##### MSC:
 17B37 Quantum groups (quantized enveloping algebras) and related deformations 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 20F36 Braid groups; Artin groups