Homology and cohomology operations in terms of differential operators

We consider some actions of the universal Steenrod algebra Q on the graded algebra of finite Laurent series L(n) in n indeterminates compatible with the familiar action of the ordinary Steenrod algebra A on the cohomology of the infinite dimensional projective space. The induced actions of the lambda algebra Λ and the Dyer–Lashof algebra R on a certain subalgebra L(n)͞ of L(n) are also studied. It turns out that the Negatively indexed generators of Q do not act as differential operators on L(n), if the Cartan formula holds. We also prove that neither Λ nor R are differential operator algebras when they act non-trivially on L(n)͞ .