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

Abstract

The extended affine Lie algebra $\widetilde{{\mathfrak{sl}}_2({\mathbb{C}}_q)}$ 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 $\widetilde{{\mathfrak{sl}}_2({\mathbb{C}}_q)}$ correspondingly. Moreover, two of these quantizations can be restricted to the extended affine Lie algebra $s{l}_2({\mathbb{C}}_q)$.

arXiv comment25 pages

References in corpus (1)

• Lie bialgebra structures on the extended affine Lie algebra $\widetilde{s{l}_2({\mathbb{C}}_q)}$