Quantizations of the Extended Affine Lie Algebra $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$

Abstract

In this paper, the extended affine Lie algebra [Formula: see text] is quantized from three different points of view, which produces three non-commutative and non-cocommutative Hopf algebra structures, and yields other three quantizations by an isomorphism of [Formula: see text] correspondingly. Moreover, two of these quantizations can be restricted to the extended affine Lie algebra [Formula: see text].