Narrow Results

Enhanced Yang–Baxter operators give rise to invariants of oriented links. We expand the enhancing method to generalized Yang–Baxter operators (gYB-operators). At present two examples of gYB-operators are known and recently three types of variations for one of these were discovered. We present the definition of enhanced generalized Yang–Baxter operators and show that all known examples of gYB-operators can be enhanced to give corresponding invariants of oriented links. Most of these invariants are specializations of the polynomial invariant P. Invariants from gYB-operators are multiplicative after a normalization.

We introduce a generalization of spin models by dropping the symmetry condition. The partition function of a generalized spin model on a connected oriented link diagram is invariant under Reidemeister moves of type II and III, giving an invariant for oriented links.