A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of the super line. As applications, solutions to the YBE are given and quandle cocycles are constructed from groupoid cocycles.
Carter, J.S.; Crans, A.; Elhamdadi, M.; and Saito, M. “Cohomology of the adjoint of Hopf algebras.” Journal of Generalized Lie Theory and Applications, Vol. 2 (2008), No. 1: 19 – 34.