TITLE: Change of basis, monomial relations, and $P_t^s$ bases for the
Steenrod algebra
AUTHOR: Ken Monks
Department of Mathematics
University of Scranton
Scranton, PA 18510
email: monks@uofs.edu
FILENAME: BASES.DVI
ABSTRACT:
The relationship between several common bases for the mod 2 Steenrod algebra
is explored and a new family of bases consisting of monomials in distinct
$P_t^s$'s 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, the new $P_t^s$ bases, and two
bases due to D. 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.