Geodesic
Quasi-triangular structures on the super-Yangian and quantum loop superalgebra and difference equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 1, pp. 129-148

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Following the V. Toledano-Laredo and S. Gautam approach we consider structures of tensor categories on analogues of the category $\mathfrak{O} $ for representations of the super Yangian $Y_ {\ hbar} (A (m, n)) $ of the special linear superalgebra Lie and the quantum loop superalgebra $U_q (LA (m, n)) $, we investigate the connection between them. The connection between Quasi-triangular structures and Abelian difference equations, which are determined by the Abelian parts of the universal R-matrices, is also described. Bibliography: 34 titles.
Keywords: Yangian of Lie superalgebra, quantum loop superalgebra, Yangian module, category of $\mathfrak{O}$ representations, Lie superalgebra, Hopf superalgebra, tensor category, difference equations.
Mots-clés : universal R-matrix, quasitriangular structure 
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     title = {Quasi-triangular structures on the {super-Yangian} and quantum loop superalgebra and difference equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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V. A. Stukopin. Quasi-triangular structures on the super-Yangian and quantum loop superalgebra and difference equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 1, pp. 129-148. http://geodesic.mathdoc.fr/item/TMF_2022_213_1_a7/