Virtual link and knot invariants from non-abelian Yang-Baxter 2-cocycle pairs

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For a given (X,S,β), where S,β X× X→ X× X are set theoretical solutions of Yang-Baxter equation with a compatibility condition, we define an invariant for virtual (or classical) knots/links using non commutative 2-cocycles pairs (f,g) that generalizes the one defined in [FG2]. We also define, a group Uncfg=Uncfg(X,S,β) and functions πf, πg X× X→ Uncfg(X) governing all 2-cocycles in X. We exhibit examples of computations achieved using GAP.