Quantum de Rham complex on 𝔸h1|2

Abstract

Introducing [Formula: see text]- and [Formula: see text]-deformations of [Formula: see text]-graded ([Formula: see text])- and ([Formula: see text])-spaces, denoted by [Formula: see text] and [Formula: see text], a two-parameter differential calculus, the quantum de Rham complex, on [Formula: see text] are explicitly constructed. It is shown that in contrast to the standard [Formula: see text]-deformation of [Formula: see text], the above complex is unique for [Formula: see text]. The quantum de Rham complex of [Formula: see text] is discussed via a contraction using standard one.