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Conditions for a module to be injective and some applications to Hopf algebra duality. (English) Zbl 0831.16024

The author presents some easily checked conditions for a module to be injective, and applies them in the situation where the module is a module algebra over a Hopf algebra \(H\), where \(H\) has polynormal augmentation ideal and every finite-dimensional simple \(H\)-module is one dimensional. The quantum group \(O_q(\text{SL}(2))\) satisfies these conditions, and the author constructs a module algebra for it. He also uses these ideas to describe the Hopf dual for \(O_q(\text{SL}(2))\) and related Hopf algebras.

MSC:

16W30 Hopf algebras (associative rings and algebras) (MSC2000)
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16D50 Injective modules, self-injective associative rings
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