The knot invariant associated to two-parameter quantum algebras

Abstract

Using the skew-Hopf pairing, we obtain [Formula: see text]-matrix for the two-parameter quantum algebra [Formula: see text]. We further construct a strict monoidal functor [Formula: see text] from the tangle category [Formula: see text] to the category [Formula: see text] of [Formula: see text]-modules. As a consequence, the quantum knot invariant of the tangle [Formula: see text] of type [Formula: see text] is obtained by the action of [Formula: see text] on the closure [Formula: see text] of [Formula: see text].