The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles

We examine the relation between Ribbon Hopf Algebras and 1-1 Tangles -- knot diagrams that are cut at a point with the ends pulled apart. Specifically, we investigate the behavior of one such algebra, introduced in the 1992 paper "On Kauffman’s knot invariants arising from finite-dimensional Hopf algebras" by David Radford. We compile the first-ever results for knots of 3-10 crossings using one of these algebras, and discuss the magnitude of calculations involved, and practical methods of attaining results in reasonable time.