Conditions for a module to be injective and some applications to Hopf algebra duality

Abstract

We present some simple conditions for a module to be injective in certain situations. Injective modules over bialgebras often have the additional structure of module algebras, and our results can be used to give some explicit examples. In particular, we construct such a module algebra for the quantum group O q ( SL ( 2 ) ) {O_q}({\text {SL}}(2)) . Our results can also be used to describe the Hopf algebra duals of O q ( SL ( 2 ) ) {O_q}({\text {SL}}(2)) and related Hopf algebras.