Quasi-triangular structures on the super-Yangian and quantum loop superalgebra and difference equations

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.