Link and knot invariants from non-abelian Yang-Baxter 2-cocycles

TL;DR

This paper introduces a new knot and link invariant based on non-abelian Yang-Baxter 2-cocycles and set-theoretical solutions, along with a universal group that classifies these cocycles.

Contribution

It defines a novel invariant using non-commutative 2-cocycles and constructs a universal group to classify all such cocycles for a given solution.

Findings

Defined a knot/link invariant from Yang-Baxter solutions and 2-cocycles

Constructed the universal group Unc(X) for classifying 2-cocycles

Provided examples demonstrating the computation of the invariant

Abstract

We define a knot/link invariant using set theoretical solutions $(X,\sigma)$ of the Yang-Baxter equation and non commutative 2-cocycles. We also define, for a given $(X,\sigma)$, a universal group Unc(X) governing all 2-cocycles in $X$, and we exhibit examples of computations.