A differential calculus on Z${}_3$-graded quantum superspace ${\mathbb{R}}_q(2|1)$

Abstract

We introduce a Z${}_3$-graded quantum $(2+1)$-superspace and define Z${}_3$-graded Hopf algebra structure on algebra of functions on the Z${}_3$-graded quantum superspace. We construct a differential calculus on the Z${}_3$-graded quantum superspace, and obtain the corresponding Z${}_3$-graded Lie superalgebra. We also find a new Z${}_3$-graded quantum supergroup which is a symmetry group of this calculus.

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Cited by in corpus (1)

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