Geodesic
Cartan--Weyl basis for $DY(sl_3)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 3, pp. 423-438

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The double of the Yangian $Y(sl_3)$ defined via Chavelly generators is constructed. The Cartan–Weyl basis ensuring an analog of the Poincare–Birkhoff–Witt theorem is obtained. This basis is used to define the action of the comultiplication on the Chavelley generators. The explicit description of the double $DY(sl_3)$ is given and the universal $R$-matrix is computed. 
@article{TMF_1997_111_3_a8,
     author = {A. V. Solov'ev},
     title = {Cartan--Weyl basis for $DY(sl_3)$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {423--438},
     publisher = {mathdoc},
     volume = {111},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_111_3_a8/}
}
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A. V. Solov'ev. Cartan--Weyl basis for $DY(sl_3)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 3, pp. 423-438. http://geodesic.mathdoc.fr/item/TMF_1997_111_3_a8/