Right-covariant differential calculus on $\mathcal{F}({\mathbb{C}}_q^{2|1})$

Abstract

We define a new ${\mathbb{Z}}_2$-graded quantum (2+1)-space and show that the extended ${\mathbb{Z}}_2$-graded algebra of polynomials on this ${\mathbb{Z}}_2$-graded quantum space, denoted by $\mathcal{F}({\mathbb{C}}_q^{2|1})$, is a ${\mathbb{Z}}_2$-graded Hopf algebra. We construct a right-covariant differential calculus on $\mathcal{F}({\mathbb{C}}_q^{2|1})$ and define a ${\mathbb{Z}}_2$-graded quantum Weyl algebra and mention a few algebraic properties of this algebra. Finally, we explicitly construct the dual ${\mathbb{Z}}_2$-graded Hopf algebra of $\mathcal{F}({\mathbb{C}}_q^{2|1})$.

24 pages

References in corpus (1)

• Left covariant differential calculi on ${\widetilde{\mathrm{GL}}}_q(2)$