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In this paper we explore the possibility of endowing simpleinfinite-dimensional ${\mathfrak{sl}_2(\mathbb{C})}$-modules by the structureof the graded module. The gradings on finite-dimensional simple module oversimple Lie algebras has been studied in [arXiv:1308.6089] and[arXiv:1601.03008].

Graded torsion-free ${\mathfrak{sl}_2(\mathbb{C})}$-modules of rank 2