Let g be a finite dimensional semisimple Lie algebra over C.The category(O)is a tensor category which contains the well-known BGG category.In this paper,we first introduce the generalized Green ring which is a natural generalization of the well-known Green ring.Then we study the explicit structure of (O)for the case g=(sl)2.Finally,we give an abelian tensor category containing(O) for(sl)2 and it is minimal in such categories.
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