Splitting Comodules over Hopf Algebras and Application to Representation Theory of Quantum Groups of Type A00

In this work we study some properties of comodules over Hopf algebras possessing integrals (co-Frobenius Hopf algebras). In particular we give a necessary and sufficient condition for a simple comodule to be injective. We apply the result obtained to the classification of representations of quantum groups of type A00.