Cartan Calculus On Hopf Superalgebra F(Ch2|1)

Abstract

In this paper, we introduce a new h-deformation of the superspace C2|1 and show that the corresponding function superalgebra F(Ch2|1) admits a Hopf superalgebra structure. Covariant first-order differential calculus on F(Ch2|1) is constructed by extending Woronowicz's and Wess-Zumino's approaches to the Z2-graded case. We also define a compatible star-structure and establish the higher-order differential calculus, inner derivations, and Lie derivatives to formulate a full Cartan calculus on F(Ch2|1). The resulting differential geometry provides a consistent framework for studying quantum Lie superalgebras and graded covariant structures on noncommutative superspaces.