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

Abstract

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