The fuzzy supersphere

We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative ₂-graded algebras tending in a suitable limit to a dense subalgebra of the ₂-graded algebra of ^∞-functions on the (2|2)-dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the super-deRham cohomology of the supersphere and the ordinary deRham cohomology of its body on the “fuzzy level”.