Cartan calculus on the superalgebra ${\cal O}({\mathbb C}_q^{2\vert1})$

Abstract

In analogy with the classical case, the noncommutative differential calculus on a quantum superspace can be extended to the Cartan calculus by introducing inner derivations and Lie derivatives. So, to give a Cartan calculus on the algebra of functions on quantum (2+1)-superspace ${\mathbb C}_q^{2\vert1}$, we first introduce two left-covariant differential calculi over ${\cal O}({\mathbb C}_q^{2\vert1})$ and extend one of these calculi by adding inner derivations and Lie derivatives to the calculus. We also introduce tensor product realization of the wedge product of forms.