Differential geometry of the Z_3-graded quantum superplane

Abstract

In this work, differential geometry of the Z${}_3$-graded quantum superplane is constructed. The corresponding quantum Lie superalgebra and its Hopf algebra structure are obtained.

16 pages

References in corpus (2)

• On the Differential Geometry of $G{L}_q(1|1)$
• Differential geometry of the q-superplane

Cited by in corpus (6)

• n=3 Nilpotent differential calculus on some non-commutative (super) spaces
• Left covariant differential calculi on ${\widetilde{\mathrm{GL}}}_q(2)$
• A differential calculus on Z${}_3$-graded quantum superspace ${\mathbb{R}}_q(2|1)$
• Cartan calculi on the quantum superplane
• The Hopf algebra structure of the Z${}_3$-graded quantum supergroup GL${}_{q,j}(1|1)$
• Right-covariant differential calculus on $\mathcal{F}({\mathbb{C}}_q^{2|1})$