Abstract: There is a general cohomology defined by Sweedler for co-commutative Hopf algebras, generalizing the usual cohomology of a group or a Lie algebra. Recently it was discovered that low-dimensional groups could be defined without the co-commutativity requirement. In joint work with Christian Kassel, we have given the first few examples of computations with these, in the case of algebras of functions on groups. These turn out to be related to torsors in algebraic geometry, and Drinfeld twists in quantum groups theory.