The hit problem for symmetric algebras over the Steenrod algebra
David Pengelley
New Mexico State University
Las Cruces, NM 88003
davidp@nmsu.edu
Frank Williams
New Mexico State University
Las Cruces, NM 88003
frank@nmsu.edu
The hit problem for a cohomology module over the Steenrod algebra A
asks for a minimal set of A-generators for the module. In this paper
we consider the symmetric algebra over the field with p elements, for p
an arbitrary prime, and treat the equivalent problem of determing the
set of A-primitive elements in its dual. We produce a method for
generating new A-primitives from known ones via a new action of the
Kudo-Araki-May algebra, K, and consider the K-module structure of the
A-primitives, which form a sub K-algebra of the dual of the symmetric
algebra over the Steenrod algebra.