Abstract
Two of the most fundamental and useful operations on the module category are the functors Hom and ⊗ from kG mo∂ × kG mo∂ to kG mo∂. The two are intimately related through duality, and they can be used to develop some interesting piece of information about the group algebra and its modules. In this section we investigate the duality and a couple of its ramifications. The most important application of the section is the proof that group algebras are self-injective algebras, and hence that the subcategories of projective and injective modules coincide.
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