Cartan calculus on the superalgebra O(Cq2| 1)

Abstract

By analogy with the classical case, noncommutative differential calculus on a quantum superspace can be extended to the Cartan calculus by introducing inner derivations and Lie derivatives. So, to give the Cartan calculus on the algebra of functions on quantum (2+1)-superspace Cq(2|) (1), we first introduce two left-covariant differential calculi over O(Cq(2|) (1)) 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.