Abstract
The weight modules of the Lie algebra are well known. In the first part of this paper we deal with a realization of weight modules of in the space , where is the algebra of Laurent polynomials. In the second part, we consider the Hom-Lie algebra of Jackson where . The q-analogue of the above realization in the space is considered. We obtain two kinds of q-modules. The regular q-modules which have limits the modules obtained in the classical realization when q goes to 1 . The other q-modules have no limits when q goes to 1 and they are called singular modules.
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