The knot invariant associated to two-parameter quantum algebras

Using the skew-Hopf pairing, we obtain $\mathcal{R}$-matrix for the two-parameter quantum algebra $U_{v,t}$. We further construct a strict monoidal functor $\mathcal{T}$ from the tangle category $($\mathrm{O}\mathrm{T}\mathrm{a}$,\otimes, \emptyset)$tothecategory$($\mathrm{M}\mathrm{o}\mathrm{d}$,\otimes, $\mathbb{Q}$(v,t))$of$U_{v,t}$-modules\mathrm{.}Asaconsequence,thequantumknotinvariantofthetangle$L$oftype$(n,n)$isobtainedbytheactionof$$\mathcal{T}$$ontheclosure$\tilde{L}$of$L$.