Change of basis, monomial relations, andPts bases for the Steenrod algebra Original Research Article

The relationship between several common bases for the mod 2 Steenrod algebra is explored and a family of bases consisting of monomials in distinctPtsʹs is developed. A recursive change of basis formula is produced to convert between the Milnor basis and each of the bases for which the change of basis matrix in every grading is upper triangular. In particular, it is shown that the basis of admissible monomials, thePts bases, and two bases due to Arnon, are all bases having this property, and the corresponding change of basis formula is produced for each of them. Some monomial relations for the mod 2 Steenrod algebra are then obtained by exploring the change of basis transformations.