Z${}_3$-graded differential geometry of quantum plane

Abstract

In this work, the Z${}_3$-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algebra and the dual algebra is given.

17 pages

Cited by in corpus (2)

• n=3 Nilpotent differential calculus on some non-commutative (super) spaces
• Right-covariant differential calculus on $\mathcal{F}({\mathbb{C}}_q^{2|1})$