Finiteness Conditions, Co-Frobenius Hopf Algebras, and Quantum Groups Original Research Article

Some finiteness conditions for infinite dimensional coalgebras, particularly right or left semiperfect coalgebras, or co-Frobenius Hopf algebras are studied. As well, examples of co-Frobenius Hopf algebras are constructed via a Hopf algebra structure on an Ore extension of a group algebra, and it is shown that bicrossproducts of co-Frobenius Hopf algebras are themselves co-Frobenius.