Left-covariant differential calculi on GL̃q(2)

Abstract

In this work, we introduce the ${\mathbb{Z}}_3$ -graded differential algebra, denoted by $\mathrm{\Omega }({\widetilde{\mathrm{G}\mathrm{L}}}_q(2))$ , treated as the ${\mathbb{Z}}_3$ -graded quantum de Rham complex of ${\mathbb{Z}}_3$ -graded quantum group ${\widetilde{\mathrm{G}\mathrm{L}}}_q(2)$ . In this sense, we construct left-covariant differential calculi on the ${\mathbb{Z}}_3$ -graded quantum group ${\widetilde{\mathrm{G}\mathrm{L}}}_q(2)$ .