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

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.Comment: 26 page

The cohomology of monogenic extensions in the noncommutative setting

We extend the notion of monogenic extension to the noncommutative setting, and we study the Hochschild cohomology ring of such an extension. As an aplication we complete the computation of the cohomology ring of the rank one Hopf algebras beggined in [S. M. Burciu and S. J. Witherspoon, Hochschild cohomology of smash products and rank one Hopf algebras].Comment: 25 pages. Some examples added, and also the Gerstenhaber structure is computed in a big family of examples, including the rank one Hopf algebra