Quantizations of the extended affine Lie algebra $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$

Abstract

The extended affine Lie algebra $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$ is quantized from three different points of view in this paper, which produces three noncommutative and noncocommutative Hopf algebra structures, and yield other three quantizations by an isomorphism of $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$ correspondingly. Moreover, two of these quantizations can be restricted to the extended affine Lie algebra ${sl_2(\mathbb{C}_q)}$.