Hopf algebra extensions of monogenic Hopf algebras Original Research Article

William M. Singer has described a cohomology theory of connected Hopf algebras which classifies extensions of a cocommutative Hopf algebra by a commutative Hopf algebra in much the same way as the cohomology of groups classifies extensions of a group by an abelian group. We compute these cohomology groups for monogenic Hopf algebras, construct an action of the base ring on the cohomology groups in the case of trivial matched pairs, and use these results to further study Singerʹs cohomology.